AP Physics C: Mechanics FRQ Room

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AP Physics C: Mechanics Free Response Questions

The best way to get better at FRQs is practice. Browse through dozens of practice AP Physics C: Mechanics FRQs to get ready for the big day.

  • View all (250)
  • Unit 1: Kinematics (40)
  • Unit 3: Work, Energy, and Power (33)
  • Unit 4: Systems of Particles and Linear Momentum (45)
  • Unit 5: Rotation (45)
  • Unit 6: Oscillations (41)
  • Unit 7: Gravitation (46)
Unit 1: Kinematics

Acceleration from a Given Velocity Function

An object moves along a straight line with its velocity described by $$v(t)= 5*t^2 - 3*t + 2$$ (m/s)

Easy

Block on an Inclined Plane: Kinematic Analysis

A block of mass m is released from rest at the top of a frictionless inclined plane of length L = 10

Easy

Coupled Motion: Translation and Rotation

A solid cylinder with mass $$m = 2.0$$ kg and radius $$R = 0.5$$ m is released from rest at the top

Extreme

Determining Motion from a Sine Position Function

An object's position is given by $$x(t)= 3*\sin(t) + t$$ (meters). Analyze its motion using calculus

Medium

Determining Velocity from a Position Function with Differentiation Error

An experiment recorded the position of a particle moving along a straight line, modeled by the funct

Hard

Differential Equation of Motion Under Gravity and Drag

A particle of mass $$m$$ is falling under gravity and experiences a drag force proportional to its v

Extreme

Displacement and Critical Points for a Time-Dependent Position Function

A particle moves along the x-axis such that its position is given by $$x(t)=4t^2 - t^3$$, where t is

Medium

FRQ 1: One‐Dimensional Constant Acceleration

An object moves along a straight line with constant acceleration. Its initial velocity is 5 m/s and

Easy

FRQ 2: Projectile Motion – Launch Experiment

A researcher uses a projectile launcher to study the flight of a ball launched at an angle. The ball

Medium

FRQ 4: Vector Addition and Displacement Analysis

A researcher studies an object moving along a straight path where its motion includes reversals in d

Easy

FRQ 6: Relative Motion in Two Dimensions (HARD)

In the xy-plane, two particles have position functions given by: $$\vec{r}_A(t)=(2*t, t^2)$$ and $$\

Hard

FRQ 7: Projectile Trajectory Analysis

A projectile is fired from ground level with an initial speed of 50 m/s at an angle of 40° above the

Easy

FRQ 11: Air Resistance and Terminal Velocity

An object of mass 2 kg is falling under gravity while experiencing air resistance proportional to it

Hard

FRQ 14: Differentiation of a Position Function

An object’s position is given by the function $$x(t)= t^3 - 6*t^2 + 9*t$$ (with x in meters and t in

Medium

FRQ 17: Analyzing Motion from a Cubic Position Function

An object’s position is given by $$x(t)= 2*t^3 - 9*t^2 + 4*t$$ (in meters, with time in seconds). An

Medium

FRQ 20: Real-World Application – Car Braking Analysis

A car traveling at 30 m/s begins braking uniformly until it comes to a complete stop. Sensors record

Hard

Impact Analysis: Collision Avoidance

Two vehicles are moving along a straight road. Vehicle A travels with constant velocity described by

Extreme

Impulse and Momentum with a Variable Force

A cart of mass $$m = 5.0\,kg$$ is subjected to a time-dependent force described by $$F(t)=5*t²$$ (in

Hard

Impulse and Variable Force Analysis

Design an experiment to measure the impulse delivered to a ball by a bat, given that the force varie

Hard

Integrating an Acceleration Function to Determine Motion

An object's acceleration is described by $$a(t)=6*t-5$$, with initial velocity $$v(0)=2$$ m/s and in

Hard

Investigating Motion on an Inclined Plane

A lab experiment was set up to study the motion of a cart on an inclined air track. The cart’s displ

Medium

Motion with Air Resistance: Approximating Terminal Velocity

A small sphere falling through a medium experiences air resistance proportional to its velocity. Its

Extreme

Newton's Second Law and Force Measurement on a Cart

Design an experiment using a cart on a frictionless track with a pulley system to verify Newton's se

Hard

Non-Uniform Acceleration Analysis

A particle's position is given by $$x(t)=\sin(t)-0.5*t^2$$. Analyze its motion using calculus.

Medium

Piecewise Motion Analysis

An object moves along a straight line with acceleration defined piecewise as follows: for $$0 \le t

Hard

Polynomial Position Function Analysis

A particle’s position along the x-axis is given by the function $$x(t)=t^3 - 6*t^2 + 9*t$$ (in meter

Medium

Projectile Launch from an Elevated Platform

A ball is launched from a platform 10 meters above the ground with an initial speed of 30 m/s at an

Medium

Projectile Motion Analysis

An object is launched with an initial speed of $$60\,m/s$$ at an angle of $$30^\circ$$ above the hor

Medium

Projectile Motion on Level Ground

An object is launched from ground level at a 45° angle with an initial speed of 30 m/s (neglect air

Easy

Projectile Motion with Air Resistance

Design an experiment to study the effect of launch angle on the horizontal range of a projectile in

Medium

Projectile Motion with Calculus Integration

An object is launched from ground level with an initial speed of 50 m/s at an angle of 40° above the

Hard

Projectile Motion: Maximum Height and Range

An object is launched from ground level at an angle of 30° above the horizontal with an initial spee

Medium

Projectile Range Analysis with Angular Misinterpretation

An experiment was conducted to analyze the range of a projectile launched at various angles. A fixed

Hard

Relative Motion Experiment

Two carts on parallel tracks move in the same direction with positions given by $$x_A(t)=5*t$$ and $

Medium

Relative Motion in Two Dimensions

A boat is moving eastward relative to the water at 5 m/s. The river current flows southward at 3 m/s

Medium

Simple Harmonic Motion in a Spring-Mass System

Design an experiment to investigate simple harmonic motion (SHM) using a spring-mass system. Describ

Easy

Sinusoidal Motion

A particle’s position along the x-axis is given by $$x(t)=8\sin(t)$$, where $$0\leq t\leq2\pi$$ (x i

Easy

Variable Acceleration Analysis Using Calculus

Design an experiment to investigate the motion of an object under a time-varying force that produces

Hard

Variable Acceleration and Integration

An object moves along a line with a time-dependent acceleration given by $$a(t)=6*t - 2$$ (in m/s²).

Medium

Variable Net Force Experiment

A cart on a frictionless track is subjected to a variable net force given by $$F(t)= 10*t$$ (N). The

Medium
Unit 3: Work, Energy, and Power

Analysis of Mechanical Advantage and Work in a Lever System

A lever is used to lift a 500 N weight. The operator applies a force that varies with the angle, giv

Medium

Conservation of Mechanical Energy with Dissipative Forces

A 1 kg ball is dropped from a height of 20 m. Experimental measurements indicate that air resistance

Hard

Damped Oscillations and Energy Dissipation in a Mass-Spring System

A damped harmonic oscillator with mass m = 2 kg, spring constant k = 50 N/m, and damping coefficient

Extreme

Energy Dissipation in a Bouncing Ball

A ball of mass 0.2 kg is dropped from a height of 2 m and rebounds to a height of 1.5 m. Assume that

Medium

Energy Dissipation in Damped Oscillations

A damped harmonic oscillator consists of a 1 kg mass attached to a spring (k = 50 N/m) with a dampin

Extreme

Energy Loss in Inelastic Collisions Experiment

Two carts on a frictionless track undergo a collision. Cart A (1 kg) moves at 4 m/s and collides wit

Medium

Equilibrium Points from a Potential Energy Function

A particle of mass 4 kg experiences a potential energy given by $$U(x) = (x - 2)^2 - (2*x - 3)^3$$ (

Hard

Experiment on Energy Loss in Frictional Systems

Design an experiment to investigate the relationship between surface roughness and energy loss durin

Medium

FRQ 11: Analysis of a Bungee Jump – Variable Net Force

A bungee jumper with a mass of 70 kg experiences a net force that changes as a function of vertical

Hard

Gravitational Potential Energy and Free Fall

A 60-kg acrobat climbs to the top of a 50-m tall platform and then jumps off. Neglecting air resista

Easy

Hydraulic Press Work Calculation Experiment

A hydraulic press compresses a metal block. The pressure in the hydraulic fluid varies with displace

Hard

Impulse and Energy Transfer via Calculus

A 2-kg object experiences a time-dependent force given by $$F(t)= 4*t$$ N for $$0 \leq t \leq 5\,s$$

Medium

Inclined Plane Friction Variation Experiment

A block is allowed to slide down an inclined plane over which the coefficient of friction is not con

Hard

Inelastic Collision and Energy Dissipation

Two blocks undergo a perfectly inelastic collision. A 3 kg block moving at 5 m/s collides with a 2 k

Easy

Investigation of Non-Conservative Forces in a Roller Coaster Model

A researcher develops a model of a roller coaster of mass 500 kg moving along a track with both grav

Hard

Kinetic Energy Change Under a Variable Force

A 2-kg object is subjected to a variable force along a horizontal path given by $$F(x)= 4 + 0.2*x \;

Medium

Kinetic Energy Measurement in a Projectile Experiment

A researcher is studying the change in kinetic energy of a small projectile. A ball of mass $$m = 0.

Easy

Potential Energy Curves and Equilibrium Analysis

An object of mass 4 kg has a potential energy function given by $$U(x) = (x - 2)^2 - (2\,x - 3)^3$$.

Extreme

Power and Efficiency in a Wind Turbine

A wind turbine with a rotor radius of 40 m extracts energy from wind. The wind speed varies with hei

Medium

Power Output in Elevator Lifting

A motor lifts an elevator of mass 500 kg at a constant speed of 2.5 m/s over a vertical displacement

Easy

Projectile Energy Analysis with Air Resistance Correction

A 0.5 kg ball is thrown vertically upward with an initial speed of 20 m/s. Air resistance does negat

Medium

Relationship Between Force and Potential Energy

For a conservative force, the relationship between force and potential energy is given by $$F(x) = -

Medium

Rotational Work and Energy Experiment

A uniform disk with a moment of inertia $$I = 0.5\,kg\cdot m^2$$ is subjected to a variable torque d

Medium

Variable Force Robotic Arm Power Experiment

In this experiment, a robotic arm exerts a time-varying force on an object as it moves along a horiz

Easy

Variable Force Work Calculation and Kinetic Energy Analysis

Consider an object moving along the x-axis under the influence of a variable force given by $$F(x) =

Medium

Variable Friction and Kinetic Energy Loss

A 5 kg block slides across a horizontal surface and comes to rest. The frictional force acting on th

Hard

Variable Gravitational Acceleration Over a Mountain

A hiker lifts a 10 kg backpack up a mountain where the gravitational acceleration decreases linearly

Hard

Work and Energy in Circular Motion

A 2-kg mass is attached to a string and constrained to move on a frictionless vertical circular path

Medium

Work by Non-Conservative Forces in a Loop

A block experiences a variable nonconservative force along a path given by $$ F(x)= 20 * \sin(x) $$

Easy

Work Done Against Friction on an Inclined Plane

A 5-kg box slides down a 10-m long inclined plane that makes an angle of 30° with the horizontal. Th

Hard

Work Done by a Variable Exponential Force

A piston is subjected to a variable force described by $$F(x)=500*\exp(-0.5*x)$$ N, where x is in me

Hard

Work Done by a Variable Gravitational Force

An object of mass 2 kg moves from a height of 50 m to 30 m above the Earth's surface. The gravitatio

Extreme

Work in a Variable Force Field along a Curved Path

A particle moves in the xy-plane along the curve defined by $$y = x^2$$ from the point (0, 0) to (2,

Extreme
Unit 4: Systems of Particles and Linear Momentum

Astronaut Recoil upon Throwing an Object

An astronaut of mass 90 kg, floating in space, throws a 1.5 kg tool directly away from her ship at 5

Easy

Ballistic Pendulum Analysis

A bullet with mass $$0.02$$ kg is fired horizontally into a pendulum bob of mass $$0.98$$ kg suspend

Medium

Center of Gravity vs. Center of Mass in a Tilted Rod

A uniform rod is supported on one end by a fulcrum. In an experiment, additional weights were placed

Medium

Center of Mass Calculation of a Non-Homogeneous Beam

A horizontal beam of length $$4$$ m has a linear mass density given by $$\lambda(x) = 5 + 4 * x^2$$

Hard

Center of Mass for Discrete Particles in the Plane

Three particles are located in the plane with the coordinates and masses given in the table below:

Easy

Center of Mass in a Coupled Mass-Spring System

Two masses (m1 = 1.5 kg and m2 = 1.5 kg) are connected by a light spring on a frictionless track. In

Easy

Center of Mass of a Variable Density Two-Dimensional Lamina

Consider a right triangular lamina with a base of length $$b$$ and a height of $$h$$. The density of

Extreme

Center-of-Mass of a Ladder with Varying Linear Density

A ladder of length $$L=2.0\,m$$ has a vertical linear mass density given by $$\lambda(y)=3.0(1+y)$$

Medium

Center-of-Mass Shift in an Internal Explosion

Three masses are arranged on a frictionless horizontal surface: m1 = 1 kg at (0,0), m2 = 2 kg at (1,

Medium

Central Force and Center-of-Mass Motion in a Binary Star System

A binary star system consists of Star A (mass $$2\times10^{30}\,kg$$) and Star B (mass $$3\times10^{

Medium

Conservation of Linear Momentum in Colliding Carts

Two carts on a frictionless track collide. Cart A (mass = 2 kg) moves to the right with a speed of 3

Easy

Derivation of the Rocket Equation Using Momentum Conservation

A rocket moving in space expels mass continuously. Assume that during an infinitesimal time interval

Extreme

Elastic Collision of Gliders

Two gliders undergo an elastic collision on a frictionless air track. Glider A (mass = 1.5 kg) is mo

Hard

Elastic Collision: Two Gliders on an Air Track

Two gliders on an air track experience a head-on elastic collision. Glider X (mass = 1 kg) initially

Hard

Explosive Separation and Momentum Conservation

A 2 kg projectile traveling at 15 m/s explodes into two equal fragments (1 kg each). One fragment mo

Hard

Explosive Separation in a Multi‐Stage Rocket

A multi‐stage rocket undergoes an explosive separation. Experimentally, Stage 1 (mass = 2000 kg) is

Extreme

FRQ 2: Center of Mass of a Composite Lamina

Consider a composite lamina composed of two rectangular regions in the xy-plane. Region A is 0.8 m b

Medium

FRQ 6: Elastic Collision Analysis

Two spheres collide elastically along a straight line. Sphere A (mass = 0.5 kg) initially moves at +

Hard

FRQ 11: Experimental Evaluation: Measurement of Center of Mass

A media report claims that a new laser-based method can determine the center of mass of irregular ob

Medium

FRQ 14: Derivation of the Continuous Center of Mass Formula

Consider a one-dimensional object with a continuous mass distribution described by the density funct

Hard

FRQ 18: Critical Evaluation: Inelastic Collision Study

A published study on vehicle collisions claims that experimental momentum measurements in inelastic

Hard

Impulse and Kinetic Energy from a Time-Dependent Force on a Car

A 1200 kg car, initially at rest, is subjected to a time-dependent force given by $$F(t)=4000 - 500*

Medium

Impulse and Work: Discerning Differences

A particle of mass 3 kg is subjected to a force that varies with position according to $$F(x)=12*x^2

Medium

Impulse from a Time-Varying Force with Graph Stimulus

A force sensor records the force applied to a hockey puck as a function of time while a player strik

Medium

Impulse from a Variable Force Function

A force acting on an object varies with time according to the function $$F(t) = 4*t^2$$ (in Newtons)

Easy

Inclined Plane: Center of Mass and Impulse Analysis

A block of mass $$3$$ kg rests on a frictionless inclined plane with an angle of $$30^\circ$$. The i

Hard

Inelastic Collision on a Frictionless Surface

Two gliders on a frictionless air track collide and stick together. Glider A (mass = 2 kg) moves rig

Medium

Inelastic Collision with a Movable Platform

A 0.3 kg ball moving horizontally at 8 m/s collides with and sticks to a 1.2 kg movable platform tha

Hard

Inelastic Collision: Combined Motion

A 0.6 kg ball moving at 4.0 m/s collides head-on with a 0.4 kg ball that is initially at rest. The b

Medium

Inelastic Collision: Two Blocks on a Frictionless Surface

Block A (mass = 5 kg, initial velocity = 2 m/s) and Block B (mass = 3 kg, initially at rest) collide

Easy

Momentum Conservation in Glider Collisions on an Air Track

In a laboratory experiment, students investigate conservation of momentum by allowing two gliders to

Medium

Motion of the Center of Mass Under an External Force

A system consists of two particles with masses 2 kg and 3 kg located at x = 0 m and x = 4 m, respect

Medium

Motion of the Center of Mass Under External Force

Consider a system consisting of two point masses connected by a light rod. Mass m1 = 2 kg is located

Medium

Multi-Dimensional Inelastic Collision Analysis

Two particles undergo a perfectly inelastic collision. Particle A (mass = 2 kg) moves with velocity

Extreme

Non-Uniform Rod Analysis

A 1.0 m long rod has a linear density given by $$\lambda(x) = 10 + 6*x$$ (kg/m) where x is measured

Easy

Oblique Collision of Ice-Hockey Pucks

Two ice-hockey pucks collide on frictionless ice. Puck A (mass = 0.2 kg) moves east at 5 m/s, and Pu

Extreme

Projectile Explosion and Center of Mass Motion

A 5 kg projectile is launched vertically upward. At its highest point, it explodes into two fragment

Hard

Ramp Push Experiment: Variable Force Integration

In a laboratory experiment, a cart on a frictionless ramp is pushed by a force that varies with time

Hard

Rocket Propulsion with Variable Mass

A rocket has an initial mass of $$M_0 = 50$$ kg (including fuel) and ejects fuel such that its mass

Extreme

Rolling Cylinder on an Incline

A uniform solid cylinder (mass = 4 kg, radius = 0.5 m) rolls without slipping down a 30° incline. An

Medium

Rotational Dynamics of a Composite Object

A composite object consists of two connected rods: Rod A is 1 m long and has uniform density, while

Extreme

Rotational Impulse in a Spinning Disc Experiment

In an experiment to measure angular impulse, a student applies a variable torque to a spinning disc

Hard

Stability of a Suspended Mobile

A suspended mobile consists of three masses hanging from strings attached to a horizontal bar. The m

Medium

Structural Stability: Crane Center of Mass Analysis

An engineer is analyzing a crane consisting of a 500-kg horizontal beam whose center of mass is at 5

Hard

Two-Ball Collision Dynamics

Two balls collide head-on in a controlled experiment. The red ball (mass = 0.5 kg) moves to the righ

Medium
Unit 5: Rotation

Acceleration of a Rotating Rigid Body with Frictional Torque

A disk with moment of inertia $$I=2\text{ kg\cdot m}^2$$ experiences a frictional torque proportiona

Medium

Analysis of Angular Displacement in a Rotating Disk

In this experiment, several dots are marked along the radius of a rotating disk. The students record

Easy

Angular Displacement and Kinematics Analysis

A researcher is investigating the kinematics of a rotating disk. The disk rotates about its center,

Easy

Angular Impulse and Change in Angular Momentum

Design an experiment to measure the angular impulse delivered to a rotating object and its resulting

Medium

Angular Kinematics Analysis Using Graphical Data

A rotating disk's angular velocity is given by the graph below. Determine key kinematic quantities f

Medium

Angular Kinematics on a Rotating Platform

A rotating platform starts from rest and accelerates with a constant angular acceleration $$\alpha$$

Easy

Combined Translational and Rotational Dynamics

A rolling disk collides elastically with a spring, causing the spring to compress before the disk re

Medium

Composite Body Rotation

A composite object is formed by welding a solid disk to a thin rod. The disk has mass $$M$$ and radi

Medium

Computational Modeling of a Spinning Disk with Variable Torque

A spinning disk with a constant moment of inertia of $$I = 0.3\,kg\,m^2$$ is subjected to a time-var

Extreme

Conservation of Angular Momentum in Explosive Separation

A rotating disk of mass $$M = 5.0 \text{ kg}$$ and radius $$R = 0.5 \text{ m}$$, spinning at $$\omeg

Hard

Coupled Rotational and Translational Dynamics in a Rolling Sphere

A sphere is allowed to roll down a curved track without slipping. The experiment examines the coupli

Hard

Cylinder Rolling on an Incline

A solid cylinder of mass M rolls without slipping down an inclined plane of height h and length L (w

Medium

Designing a Rotational System with Specified Kinetic Energy

A researcher is tasked with designing a rotational system that must store a specified amount of kine

Hard

Dynamics of a Rotating Rod with Sliding Masses

In this advanced experiment, masses are allowed to slide along a horizontal rod attached to a pivot.

Extreme

Effect of Friction on Rotational Motion

Design an experiment to quantify the torque losses due to friction in a rotating apparatus. Your goa

Medium

Effect of Variable Applied Torque on Angular Acceleration

In a controlled experiment, a variable torque is applied to a rotating disk. The resulting change in

Easy

Energy Analysis in Rolling Motion

A spherical ball of mass $$M$$ and radius $$R$$ rolls without slipping down an inclined plane of ver

Medium

Energy Dissipation Due to Friction in a Spinning Disk

A disk is spun up to a high angular velocity and then allowed to slow down due to friction. The expe

Medium

Equilibrium Analysis in a Rotating Beam System

In a lab experiment, a student investigates the equilibrium of a beam pivoted at its center with var

Medium

Equilibrium Analysis in Rotational Systems

A uniform beam is balanced on a pivot, with forces applied at various distances from the pivot to ma

Easy

Experimental Data: Angular Velocity vs Time Analysis

An experiment records the angular velocity of a rotating object over time. The provided graph shows

Medium

Experimental Investigation of Rolling Without Slipping

An experimental apparatus is used to study rolling without slipping for various cylindrical objects.

Extreme

FRQ 8: Variable Torque and Angular Acceleration

A rotating wheel with constant moment of inertia \(I = 2.00\,kg\cdot m^2\) experiences a time-depend

Hard

FRQ 19: Oscillatory Rotational Motion (Torsional Pendulum)

A torsional pendulum consists of a disk suspended by a wire. The restoring torque is given by $$\tau

Easy

FRQ 20: Time-Dependent Angular Acceleration with External Torque

A flywheel with moment of inertia \(I = 3.00\,kg\cdot m^2\) experiences an exponentially decaying ex

Hard

Influence of Friction on Rolling Without Slipping

An experiment investigates the effect of surface friction on rolling objects. The angular velocity o

Hard

Integration of Rotational Inertia: Thin Shell vs. Solid Sphere

Derive the moments of inertia for two spherical objects about an axis through their centers: (a) A

Extreme

Investigating Non-uniform Density Effects on Moment of Inertia

Design an experiment to determine the moment of inertia for an object with a non-uniform mass distri

Hard

Lever and Torque Computations

This problem involves calculating torque in a lever system. A diagram is provided below.

Easy

Mathematical Modeling of Brake Systems

A braking system applies a constant torque of $$\tau = 15 \text{ Nm}$$ on a flywheel with moment of

Medium

Parallel Axis Theorem Application in Complex Systems

A composite object consists of a uniform rod of mass $$M = 4\,kg$$ and length $$L = 3\,m$$, and an a

Medium

Parallel Axis Theorem: Composite Body Moment of Inertia

Consider a composite object consisting of a solid disk (mass $$M = 4.0 \text{ kg}$$, radius $$R = 0.

Hard

Rolling Cylinder Down an Incline

A solid cylinder rolls without slipping down an incline. A set of measurements were made at differen

Medium

Rolling Motion Dynamics Down an Incline

A solid cylinder with mass $$M = 3\,kg$$ and radius $$R = 0.2\,m$$ rolls without slipping down an in

Hard

Rolling Motion of a Sphere on an Incline

A solid sphere of mass M and radius R rolls without slipping down an inclined plane of height h star

Medium

Rolling Motion with Transition from Slipping to Pure Rolling

A solid sphere of mass m and radius R is initially sliding and rolling down an inclined plane with a

Hard

Rotational Inertia of a Composite Bead System

A researcher is investigating the effect of discrete mass distribution on the rotational inertia of

Medium

Rotational Inertia of a Non-Uniform Disk

A disk of radius R has a surface mass density given by $$\sigma(r)= \sigma_0 \left(1+\frac{r}{R}\rig

Extreme

Rotational Inertia of a Uniform Rod

A uniform, thin rod of length $$L$$ and mass $$m$$ rotates about an axis perpendicular to the rod th

Medium

Rotational Kinetic Energy Storage in a Flywheel

An engineer is tasked with designing a flywheel energy storage system. The flywheel is required to s

Extreme

Time-varying Angular Acceleration in a Rotational System

A disk experiences an angular acceleration described by $$\alpha(t)=5\sin(2t) \text{ rad/s}^2$$.

Hard

Time-Varying Torque and Angular Acceleration

A researcher is exploring the effects of a time-varying torque on the rotational motion of a rigid b

Hard

Torque and Rotational Inertia: Uniform Rod

A uniform rod of length $$L = 2.0 \text{ m}$$ is pivoted about one end. A force of $$F = 10 \text{ N

Medium

Torque on a Lever Arm

A lever arm is used to apply force at an angle. Consider a force of $$50*N$$ applied at an angle of

Easy

Torque, Friction, and Rotational Equilibrium in a Pulley

A pulley with radius 0.3 m and moment of inertia 0.15 kg m^2 is subjected to a tangential force of 2

Medium
Unit 6: Oscillations

Calculus Derivative Analysis in SHM

Given an oscillator with a position function $$y = 0.05 \sin(12t + \frac{\pi}{6})$$, where $$y$$ is

Hard

Calculus-Based Prediction of Maximum Speed

A photogate system is set up to record the speed of a mass-spring oscillator. Answer the following p

Easy

Comparative Analysis of Horizontal and Vertical SHM Systems

A researcher compares the oscillations of a mass attached to a spring in horizontal and vertical con

Medium

Comparative Dynamics of Mass-Spring and Pendulum Oscillators

Analyze the motion of two oscillatory systems: a mass-spring oscillator and a simple pendulum (using

Extreme

Comparison of Horizontal and Vertical Oscillations

Compare a mass-spring oscillator on a frictionless horizontal surface with a vertical spring-block s

Medium

Complex SHM: Superposition of Two Harmonic Motions

A block experiences two independent harmonic motions such that its displacement is given by $$x(t)=

Hard

Composite Oscillator: Two Springs in Series

A block with mass $$m = 1.0\,kg$$ is attached to two springs connected in series, with spring consta

Hard

Deriving the General Solution of SHM

Derive and analyze the general solution for simple harmonic motion from the governing differential e

Easy

Determination of Angular Frequency from Displacement Data

Displacement measurements for a spring-mass oscillator are given by the equation $$y = A\sin(\omega

Medium

Determination of the Spring Constant from Experimental Force-Displacement Data

In an experiment to determine the spring constant, a series of force and displacement measurements w

Medium

Determining Oscillation Frequency from Acceleration Data

An accelerometer attached to a mass-spring system records acceleration data during oscillations. The

Medium

Determining Spring Constant from Force-Displacement Data

In a laboratory experiment, the force exerted by a spring is measured for various displacements. The

Easy

Energy Conservation in a Mass–Spring Oscillator

Examine energy conservation in a mass–spring system and its experimental verification.

Medium

Energy Conservation in a Simple Pendulum

A simple pendulum of length $$L$$ and mass $$m$$ is displaced by a small angle $$\theta$$ from the v

Hard

Energy Distribution and Phase Analysis

An experiment on a spring-mass oscillator is conducted to study the distribution of kinetic and pote

Medium

Energy Transformations in SHM

Consider a block attached to a spring undergoing simple harmonic motion with displacement $$x(t)=A\s

Medium

Experimental Analysis of SHM Data

The displacement data for a mass-spring system were recorded during a laboratory experiment. The fol

Medium

FRQ 2: Energy Conversion in a Spring Oscillator

A block attached to a spring oscillates on a frictionless surface. The following table presents expe

Medium

FRQ 9: Damped Oscillatory Motion Analysis

An oscillator experiencing damping shows a decrease in amplitude over successive cycles. Analyze the

Hard

FRQ 16: Maximum Speed in SHM via Energy Methods

Experimental data for a mass–spring oscillator, including amplitude, mass, spring constant, and meas

Medium

FRQ 17: Determination of Damping Coefficient

An oscillatory system exhibits damping, with its amplitude decreasing over successive cycles. Analyz

Hard

FRQ3: Kinematics of SHM – Period and Frequency

A block-spring oscillator is observed to take 0.4 s to travel from its maximum displacement in one d

Easy

FRQ6: Calculus Derivation of Velocity and Acceleration in SHM

For a mass undergoing simple harmonic motion described by the displacement function $$x(t)= A\sin(\o

Hard

FRQ12: Phase Shift and Time Translation in SHM

An oscillator is described by the equation $$x(t) = A\sin(\omega t+\phi_0)$$. Answer the following:

Hard

FRQ20: Energy Dissipation in Damped Pendulum Oscillations

A damped pendulum oscillates with small angles such that its motion is approximately described by $

Hard

Graphical Analysis of SHM Experimental Data

A block attached to a horizontal spring oscillates, and its displacement $$x(t)$$ (in meters) is rec

Medium

Horizontal Mass-Spring Oscillator Analysis

A laboratory experiment involves a block of mass $$m = 0.50\,kg$$ attached to a horizontal spring of

Easy

Lagrangian Mechanics of the Simple Harmonic Oscillator

A researcher employs Lagrangian mechanics to analyze a mass-spring oscillator. Consider a mass $$m$$

Extreme

Mass-Spring Differential Analysis

Consider a block of mass $$m$$ attached to a horizontal spring with spring constant $$k$$. The block

Medium

Oscillations of a Liquid Column in a U-tube

A U-tube containing a liquid with density $$\rho$$ exhibits oscillatory motion when the liquid is di

Hard

Pendulum Approximation and Small-Angle Motion

A simple pendulum of length $$L$$ oscillates with small amplitude. Using the small-angle approximati

Medium

Pendulum Motion: Small Angle Approximation and Beyond

A simple pendulum consists of a mass $$m = 0.3 \; kg$$ attached to a massless rod of length $$L = 1.

Easy

Pendulum Oscillation Experiment: Frequency and Energy Analysis

A simple pendulum consists of a bob of mass $$m = 0.2\;kg$$ attached to a massless string of length

Medium

Pendulum Period Measurement Experiment

A group of students measure the period of a simple pendulum by timing multiple oscillations using a

Easy

Phase Constant and Sinusoidal Motion

A mass-spring system oscillates according to $$x(t) = A \sin(\omega t + \phi_0)$$ with an amplitude

Hard

Phase Space Analysis of SHM

A student plots the phase space diagram (velocity vs. displacement) of a simple harmonic oscillator

Hard

Sinusoidal Oscillator and Phase Constant

A mass attached to a spring oscillates horizontally on a frictionless surface, and its displacement

Hard

Spring-Block Oscillator: Phase Angle and Motion Description

A block attached to a horizontal spring oscillates without friction. The motion of the block is desc

Medium

Systematic Error Analysis in SHM Experiments

The table below shows measured time intervals and displacements from several trials in an experiment

Extreme

Time-Dependent Length in a Variable-Length Pendulum

In an experiment, a pendulum has a length that varies with time according to the relation $$L(t)=L_0

Hard

Vertical Mass-Spring Oscillator: Equilibrium and Oscillations

A 2.0-kg mass is attached to the end of a vertical spring with a force constant $$k = 250\,N/m$$. Th

Medium
Unit 7: Gravitation

Analysis of a Gravitational Potential Energy Graph

A graph representing gravitational potential energy as a function of distance is provided below. The

Hard

Analyzing a Two-Body Gravitational Interaction Using Calculus

Consider two objects of masses $$m_1$$ and $$m_2$$ that are initially at rest and start moving towar

Hard

Areal Velocity and Angular Momentum in Planetary Motion

A planet of mass $$m$$ orbits a star while conserving its angular momentum $$L$$. Answer the followi

Medium

Average Orbital Energy and Angular Momentum

For an orbiting satellite, the specific orbital energy and angular momentum are key conserved quanti

Hard

Cannonball Trajectory in a Non-Uniform Gravitational Field

An experiment studies the trajectory of a cannonball launched at a high angle to analyze projectile

Medium

Center of Mass in a Two-Body System

In a two-body system, such as a planet and its moon, both bodies orbit around their common center of

Medium

Comparative Analysis of Orbital Periods for Different Planets

Two planets orbit a star. (a) Derive the relationship $$\frac{T^2}{a^3} = \text{constant}$$ for thes

Easy

Comparative Analysis of Planetary Orbits

Two planets orbit the same star with different semimajor axes. Use Kepler's Third Law to analyze and

Medium

Deriving Gravitational Potential from Gravitational Force

The gravitational potential \(V(r)\) is related to the gravitational force by calculus. (a) Show th

Medium

Determining the Center of Mass in a Celestial System

In studying the two-body problem, such as the Sun-planet system, the center of mass (or barycenter)

Easy

Dynamics of a Binary Star System

Binary stars orbit around their common center of mass. Consider two stars with masses $$M_1$$ and $$

Hard

Elliptical Orbit Simulation Error in Barycenter Consideration

A computer simulation is developed to mimic the elliptical orbits of planets using Newton's law of g

Hard

Energy Balance at Apoapsis and Periapsis

Analyze the provided energy data for a planet at apoapsis and periapsis in its orbit. Discuss how co

Hard

Energy Conservation in a Swinging Mass Experiment

An experiment is performed wherein a mass is swung in a vertical circle to investigate conservation

Medium

Energy Conversion in a Gravitational Slingshot Maneuver

A spacecraft performing a gravitational slingshot maneuver around a planet converts gravitational po

Hard

Energy Dissipation in Orbital Decay

A satellite experiences a tangential drag force given by $$F_{drag} = -b * v$$, where $$b$$ is a con

Extreme

Escape Velocity and Energy Conservation

Consider an object of mass m escaping from a planet with mass M, where gravitational potential energ

Medium

Escape Velocity Derivation

A spacecraft of mass m is located on the surface of a planet with mass M and radius R. Using energy

Medium

Free Fall with Air Resistance: Integral Approach

A free-fall experiment is performed in a laboratory where a sphere is dropped and its position is re

Easy

FRQ 10: Gravitational Interactions in a Three-Body System

Consider a simplified system with three masses, $$m_1$$, $$m_2$$, and $$m_3$$, located at fixed posi

Extreme

FRQ 11: Time-Dependent Gravitational Force in Radial Motion

A spaceship travels radially away from a planet under the influence of gravity. Consider the gravita

Hard

Graphical Analysis of Gravitational Force Variation

A set of experimental data shows how gravitational force varies with distance between two masses. An

Medium

Gravitational Analysis of a Composite Mass Distribution

A researcher studies the gravitational field of an irregular object composed of two connected sphere

Extreme

Gravitational Energy in a Binary Star System

Binary star systems are bound by gravity. The total mechanical energy of such a system includes kine

Hard

Gravitational Interaction between Two Bodies

Consider two masses m1 and m2 separated by a distance r in deep space. Investigate the gravitational

Easy

Gravitational Parameter in Exoplanetary Systems

Using the provided exoplanetary data, analyze the consistency of the gravitational parameter (derive

Extreme

Gravitational Potential Energy in a Non-Uniform Field

A spacecraft of mass m moves radially from a distance R₀ to a distance R from a planet of mass M. Th

Hard

Gravitational Potential Energy Measurement on a Roller Coaster

An amusement park ride features a roller coaster that reaches a maximum height of $$50 \;m$$ above t

Medium

Gravitational Slingshot Maneuver

A spacecraft uses a gravitational slingshot maneuver to gain speed by passing near a planet. (a) Des

Hard

Gravity Assist in Three-Body Dynamics

In a gravitational slingshot (gravity assist) maneuver, a spacecraft can change its velocity by inte

Extreme

Integration of Variable Gravitational Force over an Extended Body

Consider a uniform rod of length L and total mass m, oriented radially away from the center of a pla

Extreme

Investigating Tidal Forces in a Binary Star System

Tidal forces in binary star systems can have significant effects on the stars’ structures. Answer th

Extreme

Laboratory Test of Newton's Law of Gravitation using a Torsion Balance

Newton's Law of Gravitation can be tested in a laboratory setting using sensitive apparatus such as

Hard

Modeling Orbital Decay due to Atmospheric Drag

A low Earth orbit satellite experiences orbital decay primarily due to atmospheric drag. The drag fo

Hard

Orbit Stability from Potential Energy Diagrams

Analyze the provided potential energy diagram and determine the regions corresponding to stable and

Hard

Orbital Dynamics: Gravitational Force Variation

Examine the following experimental evidence on the gravitational force as a function of distance for

Easy

Orbital Energy and Conservation Laws

For a satellite in a circular orbit of radius $$r$$ around a planet, the kinetic energy is given by

Medium

Orbital Motion of a Satellite

A satellite of mass m is in a stable circular orbit around a planet of mass M at a distance r from t

Medium

Orbital Periods and Kepler's Third Law

Kepler's Third Law states that the ratio $$\frac{T^2}{a^3}$$ is constant for planets orbiting the sa

Hard

Orbital Perturbation due to Radial Impulse

A satellite in a circular orbit of radius R receives a small radial impulse, altering its orbit into

Hard

Orbital Perturbations from Impulsive Thrust

A satellite in a circular orbit of radius $$r$$ receives an impulsive radial thrust with magnitude $

Extreme

Orbital Speed Variation in Elliptical Orbits

Analyze the provided data on orbital speeds at different points in an elliptical orbit. Discuss how

Hard

Satellite Orbital Decay with Atmospheric Drag Consideration

An experiment is designed to measure the decay of a satellite's orbit by tracking its altitude over

Medium

Simulating Satellite Orbital Decay and Atmospheric Drag

An experimental simulation is set up to study the orbital decay of a satellite due to atmospheric dr

Extreme

Variation of Gravitational Force with Distance

Newton’s Law of Gravitation indicates that the gravitational force between two masses varies inverse

Medium

Work Done in a Variable Gravitational Field

An object of mass $$m$$ is moved radially from a distance $$r_1$$ to $$r_2$$ in the gravitational fi

Medium

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FAQWe thought you might have some questions...
Where can I find practice free response questions for the AP Physics C: Mechanics exam?
The free response section of each AP exam varies slightly, so you’ll definitely want to practice that before stepping into that exam room. Here are some free places to find practice FRQs :
  • Of course, make sure to run through College Board's past FRQ questions!
  • Once you’re done with those go through all the questions in the AP Physics C: MechanicsFree Response Room. You can answer the question and have it grade you against the rubric so you know exactly where to improve.
  • Reddit it also a great place to find AP free response questions that other students may have access to.
How do I practice for AP AP Physics C: Mechanics Exam FRQs?
Once you’re done reviewing your study guides, find and bookmark all the free response questions you can find. The question above has some good places to look! while you’re going through them, simulate exam conditions by setting a timer that matches the time allowed on the actual exam. Time management is going to help you answer the FRQs on the real exam concisely when you’re in that time crunch.
What are some tips for AP Physics C: Mechanics free response questions?
Before you start writing out your response, take a few minutes to outline the key points you want to make sure to touch on. This may seem like a waste of time, but it’s very helpful in making sure your response effectively addresses all the parts of the question. Once you do your practice free response questions, compare them to scoring guidelines and sample responses to identify areas for improvement. When you do the free response practice on the AP Physics C: Mechanics Free Response Room, there’s an option to let it grade your response against the rubric and tell you exactly what you need to study more.
How do I answer AP Physics C: Mechanics free-response questions?
Answering AP Physics C: Mechanics free response questions the right way is all about practice! As you go through the AP AP Physics C: Mechanics Free Response Room, treat it like a real exam and approach it this way so you stay calm during the actual exam. When you first see the question, take some time to process exactly what it’s asking. Make sure to also read through all the sub-parts in the question and re-read the main prompt, making sure to circle and underline any key information. This will help you allocate your time properly and also make sure you are hitting all the parts of the question. Before you answer each question, note down the key points you want to hit and evidence you want to use (where applicable). Once you have the skeleton of your response, writing it out will be quick, plus you won’t make any silly mistake in a rush and forget something important.