AP Physics 1: Algebra-Based FRQ Room

Acceleration from a Velocity-Time Graph

A velocity vs. time graph is provided for an object moving along a straight line, represented by the

Analysis of a Velocity-Time Graph

Examine a velocity vs time graph of an object to analyze its motion characteristics.

Analyzing a Cyclist's Journey

A cyclist's route is divided into five segments with the following details: | Segment | Distance (k

Analyzing Non-Uniform Acceleration from a Velocity-Time Graph

This question challenges you to analyze a velocity-time graph with non-uniform acceleration. Refer t

Average Speed vs. Average Velocity on a Circular Track

This question investigates the difference between average speed and average velocity. Consider a car

Calculating Acceleration in Uniformly Accelerated Motion

A car, starting from rest, accelerates uniformly and reaches a final velocity of $$24$$ m/s in $$8$$

Calculating Car Stopping Distance and Reaction Time Effects

Analyze the stopping distance of a car incorporating both braking and driver reaction time.

Circular Motion: Speed vs Velocity

A runner completes one lap around a circular track with a circumference of 400 m at a constant speed

Comparative Analysis of Scalar and Vector Quantities in Experiment

An experiment records the following measurements: a mass of 2 kg, a temperature of 25°C, a velocity

Comparing Scalar and Vector Quantities

An experiment records both the scalar speed and the vector velocity of an object during several tria

Comparing Speed and Velocity in a Track Experiment

In this field experiment, runners’ motions on a curved track are recorded using GPS sensors. The pro

Determining Average Velocity and Instantaneous Acceleration from a Graph

A position vs. time graph is provided. Analyze it to answer the following questions.

Determining Displacement from Variable Velocity Data

A series of measurements of an object's velocity at different times is given in the table below. Usi

Distance and Displacement Conceptual Analysis

A car travels along a curved route such that the total distance traveled is $$200\ m$$, while its ne

Distance vs. Displacement in Multiple Path Travel

An object is moved from point A to point B following an L-shaped path. The path consists of two perp

Drone Delivery Route

A delivery drone flies from a warehouse to a customer's location. Its flight path is not a straight

Effect of Air Resistance on Downward Motion Experiment

In this experiment, two objects with identical masses but different shapes (a flat plate and a spher

Effect of Launch Angle on Maximum Height

Develop an experiment to determine how varying the launch angle of a projectile affects its maximum

Elevator Motion Analysis

An elevator in a multi-story building exhibits varying motion: starting from rest, accelerating, mov

Evaluating Experimental Data on Uniform Acceleration Using the BIG FIVE Equations

An experiment is conducted to study uniformly accelerated motion. Data for time, velocity, and displ

Everyday Vector and Scalar Quantities

Consider the following physical quantities: mass, displacement, time, speed, and temperature. Identi

Experimental Design: Distance vs. Displacement Lab

A researcher is designing an experiment to investigate the differences between distance and displace

Free Fall Acceleration Measurement Error

A student performs an experiment to measure gravitational acceleration $$g$$ by dropping a small ste

Free Fall Experiment Analysis

In a free fall experiment, an object is dropped from rest and the distance fallen is recorded at var

Free Fall from a Building

An object is dropped from rest from the top of a 45 m tall building.

Free Fall Motion and Gravitational Acceleration

In a free fall experiment, an object is dropped from various heights and the time taken to reach the

Friction Effects on Uniform Motion: Velocity Decay Study

A report claims that an object moving horizontally experiences zero net force and maintains constant

Friction in Inclined Plane Experiment Error

A student sets up an experiment on an inclined plane to determine the coefficient of kinetic frictio

Graphical Interpretation: Relationship between Position, Velocity, and Acceleration

An experiment provides three graphs of an object’s motion: • Graph A: Position vs. Time • Graph B:

Interpreting a Position vs Time Graph

A position vs. time graph for a moving car is provided in the stimulus. The graph displays three dis

Interpreting a Velocity vs. Time Graph

A velocity vs. time graph of an object’s motion is provided. Answer the following:

Interpreting Position vs. Time Graphs

A position vs. time graph for a moving object is provided. Use the graph to answer the following:

Investigating Initial Velocity in Uniform Acceleration

Design an experiment to investigate how different initial velocities affect the displacement of an o

Jogger's Path Analysis: Distance and Displacement

A local news article reports that a jogger's displacement during his run was equal to the total dist

Kinematics of a Multistage Journey

An object undergoes a two-stage journey. In stage 1, it travels from point A to point B covering $$2

Motion Analysis on an Inclined Plane

A block slides down a frictionless inclined plane that makes an angle of $$20^\circ$$ with the horiz

Motion on an Inclined Plane

A block slides down a frictionless inclined plane with an acceleration of $$3.5$$ m/s^2. Starting fr

Motion on an Inclined Plane

A block slides down a frictionless inclined plane with a constant acceleration. Analyze its motion a

Motion on an Inclined Plane

A 2 kg block slides down a smooth, frictionless inclined plane making a 30° angle with the horizonta

Motion with Changing Acceleration

An object moves along a straight line with a time-dependent acceleration given by $$a(t) = 2*t - 3$$

Non-Uniform Acceleration: Qualitative Analysis

A researcher investigates the launch of a model rocket. A Position vs. Time graph shows a non-linear

Position vs Time Graph Analysis

A position vs. time graph for an object in one-dimensional motion is provided. Answer the following

Projectile Motion Analysis

A ball is launched at an angle of $$30^\circ$$ above the horizontal with an initial speed of $$20\ m

Projectile Motion Experiment Design

Design a controlled experiment to investigate the effects of launch angle on the range of a projecti

Projectile Motion Experiment: Angle of Launch

Design an experiment to investigate how the angle of launch affects the range of a projectile. Your

Projectile Motion Launch Error

A student sets up a projectile launcher to study the range of a ball. The launcher is fixed at a spe

Projectile Motion: Angle and Range Optimization

Analyze a projectile launched with an initial speed $$v_0$$ from the ground. Answer the following pa

Projectile Motion: Launched Ball

A ball is launched from ground level at an angle of $$30^\circ$$ with an initial speed of $$20\,m/s$

Projectile Motion: Maximum Height Determination

A ball is launched at different angles while keeping the initial speed constant. The maximum heights

Time-Dependent Acceleration Analysis

A car's acceleration is given by the function $$a(t)=3-0.5*t$$ for $$0 \leq t \leq 6 \; s$$. Analyze

Track Run Analysis: Distance vs. Displacement

A runner on a school track completes one full lap around a curved circuit. Although the runner's pat

Uniform Acceleration Analysis Using BIG FIVE Equations

A car starting from rest accelerates uniformly. Data for a trial is provided below. Use the provided

Uniform Acceleration Analysis using the BIG FIVE Equations

A car accelerates uniformly from rest for a period of 10 seconds. This experiment uses the BIG FIVE

Uniform Acceleration Measurement Experiment

In an investigation of uniform acceleration, a cart is launched along a smooth, frictionless track a

Uniform Acceleration with Variable Initial Velocities

Two vehicles start moving with different initial velocities but share the same constant acceleration

Uniform and Non-Uniform Acceleration: Evaluating a Claim

A claim has been made that the BIG FIVE equations of motion can be applied even when an object exhib

Uniformly Accelerated Car

A car starting from rest accelerates uniformly along a straight road and then decelerates uniformly

Uniformly Accelerated Motion with the BIG FIVE Equations

This question requires you to apply the BIG FIVE equations of motion to analyze uniformly accelerate

Uniformly Accelerated Motion: Big Five Equations

A car accelerates uniformly from rest to a speed of 30 m/s over a period of 10 seconds. Use the stan

Uniformly Accelerated Motion: Car Acceleration

A car starts from rest and accelerates uniformly. The following table shows the car's velocity measu

Uniformly Accelerated Motion: Deriving Equations

Derive the kinematic equation for displacement under uniform acceleration, $$s = ut + \frac{1}{2}at^

Validation of Projectile Motion Equations

In an experiment on projectile motion, measured ranges and theoretical ranges were recorded for thre

Vector Addition and Net Displacement

A traveler moves according to three displacement vectors: $$\vec{d_1} = (3, 4)\, m$$, $$\vec{d_2} =

Vector and Scalar Quantities

Answer the following questions regarding vector and scalar quantities in physics.

Vector and Scalar Quantities in Motion

In a motion experiment, a sensor recorded the velocity of an object as a function of time. Using the

Vibrational Motion and Simple Harmonic Motion (SHM) Experiment

A mass-spring system is used to investigate simple harmonic motion. The period of oscillation is rec

Analyzing a Car Crash: Friction, Inertia, and Safety

A transportation safety study claims that an abrupt car stop during a crash can be perfectly modeled

Analyzing Friction Forces in a Sled on Snow

A sled of mass $$m = 20 * (kg)$$ is sliding on a snowy surface where the coefficient of kinetic fric

Analyzing Impulse in a Collision

During a collision experiment, the force exerted as a function of time is recorded, and the graph be

Applied Force Direction and Acceleration

Design an experiment to investigate how the angle at which a force is applied affects the accelerati

Applying Newton's Second Law

Investigate Newton's Second Law through both theoretical derivation and experimental data.

Block on an Inclined Plane with Friction Analysis

A block of mass $$m$$ slides down an inclined plane with an angle $$\theta$$. The coefficient of kin

Centripetal Force in Circular Motion

Explore the dynamics of circular motion and the associated centripetal force acting on an object.

Comparing Gravitational and Inertial Mass in an Experiment

A researcher aims to compare gravitational mass (as determined by weight and pendulum oscillations)

Designing a Newton’s Cradle Experiment

Newton’s cradle demonstrates conservation of momentum and Newton's third law. Analyze its dynamics.

Dynamics Experiment 5: Dynamic Force Sensor Calibration

A student performs an experiment using a digital force sensor to quantify the net force acting on a

Dynamics Experiment: Analyzing Net Force on an Accelerating Elevator

An elevator is accelerated upward by a motor and its acceleration is measured. The net force acting

Dynamics FRQ #5: Projectile Motion with Air Resistance

A ball of mass 2.0 kg is projected horizontally from a 45 m high building with an initial speed of 1

Dynamics FRQ #7: Investigating Inertial Mass with a Force Sensor

A student performs an experiment to measure inertial mass. Using a force sensor, the student applies

Dynamics FRQ #17: Two-Block Spring System

Two blocks of masses 2.0 kg and 3.0 kg are connected by a light spring with a spring constant of 200

Dynamics FRQ #19: Gravitational vs. Inertial Mass

In an experiment, two objects with gravitational masses $$m_1 = 2.0\,kg$$ and $$m_2 = 3.0\,kg$$ are

Dynamics in Non-Inertial Frames

A small mass is placed on a rotating laboratory platform with an angular acceleration of 0.5 rad/s²

Dynamics of a Blasting Car Propelled by Explosive Force

A car on a frictionless track is propelled by a controlled explosion that delivers an impulse over a

Dynamics of a Block on an Incline with Applied Force

An experiment investigates the motion of a block on an inclined plane while an additional force is a

Dynamics of a Car on a Banked Curve

A car with mass $$m = 1500 ~kg$$ negotiates a banked curve of radius $$R = 50 ~m$$ that is inclined

Dynamics of a Car Skidding on a Curve

A car with mass $$m = 1200 ~kg$$ is taking a circular curve with a radius of $$R = 30 ~m$$ at a spee

Dynamics of a Cart on a Frictional Track

In a laboratory experiment, a researcher uses a cart moving on a horizontal track to study the relat

Dynamics of a Falling Object with Air Resistance

Consider a falling object of mass $$m = 1 * kg$$ experiencing gravitational force and air resistance

Dynamics of a Rotating System: Loop-the-Loop Analysis

In a loop-the-loop experiment, a small object of mass 0.5 kg moves through loops of different radii.

Dynamics of a Suspended Mass: Tension Analysis

A mass \(m\) is suspended by a rope. Analyze the forces acting on the mass when it is at rest and wh

Dynamics Problem 18: Effects of Air Resistance on Free-Fall

An object in free-fall is subject not only to gravity but also to a constant air resistance force $$

Evaluating Dynamic Equilibrium: Forces and Acceleration

A researcher examines objects moving at a constant velocity (dynamic equilibrium) on a horizontal su

Exploring Inertia with Varying Mass Distributions

Students investigate how the distribution of mass in a rotating object affects its moment of inertia

Frictional Force and Acceleration Experiment

Students investigate the relationship between applied force and acceleration on a dynamics cart by a

FRQ5: Dynamics on an Inclined Plane

A cart is allowed to slide down a nearly frictionless inclined plane at varying angles. Study the da

FRQ6: Analyzing Frictional Forces

An experiment measures the frictional force on a moving object for different normal forces. Use the

FRQ18: Constant Force and Varying Mass

An experiment uses a constant applied force of 10 N on objects of different masses. The resulting ac

Interpreting a Diagram with Force Discrepancies

A diagram is provided that purports to show all the forces acting on a block on a sloped surface, bu

Investigating Friction in Rotating Systems

A researcher studies the deceleration of a spinning disc due to friction. The goal is to determine t

Investigating Inertial Mass through Force Application Experiments

A student runs an experiment to measure inertial mass by applying different known forces to an objec

Investigating Tension in a Two-Mass Pulley System

Design an experiment using a two-mass pulley system (Atwood machine) to measure the tension in the c

Momentum and Collision Dynamics

Collisions involve action-reaction forces and momentum conservation. Consider a head-on collision sc

Motion on an Inclined Plane

A block is placed on a frictionless inclined plane that makes an angle $$\theta$$ with the horizonta

Motion Under Variable Friction Conditions

A student studies the effect of different surface textures on the acceleration of a sliding object.

Pendulum Experiment for Gravitational Acceleration

A student sets up a pendulum with a long string and heavy bob to measure the gravitational accelerat

Projectile Motion and Launch Angle Optimization

Design an experiment to study projectile motion by varying the launch angle, with the aim of determi

Projectile Motion Dynamics with Air Resistance

A projectile is launched horizontally, and its horizontal displacement is measured at different time

Projectile Motion with Air Resistance Idealization

A projectile is launched with an initial speed $$v_0 = 20 * m/s$$ at an angle $$\theta = 30°$$ above

Pulley System Verification of Newton’s Second Law

A student uses a pulley system in which a cart on a track is connected to a hanging mass. Different

Quantitative Analysis of Tension Variation in a Pulley System

In a two-mass pulley system, a researcher analyzes the forces acting on each mass and the tension in

Relationship Between Applied Force and Acceleration

A student performs an experiment on a single object by applying different forces and measuring the r

Verifying Newton's Second Law in a Lab Experiment

In a lab experiment, a cart on a frictionless track is subjected to different applied forces. The ac

Analyzing Circular Motion in a Race Car Turn

A race car with a mass of 800 kg is negotiating a circular turn of radius 50 m at a constant speed o

Analyzing Gravity Measuring Apparatus Data

A student builds a gravity measuring apparatus that relies on timing the free fall of a small ball t

Ball on a String Dynamics

A ball of mass $$m = 0.2\,kg$$ is attached to a string of length $$L = 1.5\,m$$ and is swung so that

Centrifuge Dynamics

A laboratory centrifuge spins a sample in a tube along a circular path of radius $$r$$ at a constant

Comparing Gravitational and Electric Force in Microscale Systems

In a laboratory experiment, two microscale spheres are suspended near each other. Each sphere has a

Comparing Gravitational and Electric Forces

Two scenarios are considered on a lab bench: (1) two small spheres, each of mass 0.1 kg, are 0.5 m a

Comparing Orbital Motion with Circular Motion on Earth

A comparative study has compiled data from satellites in orbit and vehicles navigating circular test

Crank-Driven Oscillatory System

A mechanical system uses a rotating crank to drive a piston. The crank has a radius of $$r = 0.1 \;m

Effects of Angular Speed on Apparent Weight in a Rotating System

In a rotating space station designed to simulate gravity, the apparent weight felt by occupants resu

Examining the Effects of Altering Angular Speed on Apparent Weight

In a centrifuge, a sample experiences a change in its apparent weight as the rotational speed increa

Free Fall vs Circular Motion: Misinterpretation of Forces

A student attempts to measure and compare the acceleration of an object in free fall with that of an

Gravitational vs Electric Force Experiment: Conceptual Error Analysis

A group of students designs an experiment to compare gravitational and electric forces acting on sma

Investigation of Free-Fall Motion

In a vacuum chamber, objects are dropped from a known height of 20 m. The recorded free-fall times f

Orbital Mechanics and Gravitational Forces of Binary Stars

Astronomers observe binary star systems and record their orbital periods and separations. A logarith

Orbital Speed Variation in Circular Orbits

A student uses a computer simulation to study the orbital speeds of satellites in circular orbits ar

Pendulum Motion in a Vertical Circle

A pendulum bob of mass 2 kg is attached to a string of length 3 m and moves in a vertical circle. At

Uniform Circular Motion of a Ball on a String

A ball of mass $$m = 0.5 \;kg$$ is attached to a string and swung in a horizontal circle of radius $

Uniform Circular Motion of a Car on a Circular Track

A car of mass m drives along a circular track at constant speed. Analyze the forces involved in this

Water Park Slide Centripetal Dynamics

At a water park, a curved slide features a circular arc section with a fixed radius of $$r = 5\,m$$.

Analysis of Power in an Oscillatory System

A mass-spring system oscillates with a mass of $$2 kg$$ attached to a spring of constant $$200 N/m$$

Analysis of the Work-Energy Theorem in Motion

A 2 kg block slides on a horizontal surface and comes to rest after traveling 10 m. Its initial velo

Analyzing the Work-Energy Theorem through a Spring Launch Experiment

In this experiment, a spring launcher propels a mass horizontally. The spring is compressed a known

Analyzing Work in Systems with Changing Forces

A force that varies with displacement is defined as $$F(x)= 10 * \sin(x)$$ (in N) for x in meters, w

Block on Rough Surface

A 3 kg block is projected with an initial speed of 7 m/s on a horizontal rough surface. It travels 8

Block Sliding on a Rough Surface: Friction Work

A 5 kg block slides on a rough horizontal surface. It is given an initial speed of 8 m/s and comes t

Conservation of Energy in a Bouncing Ball

A 0.3 kg ball is dropped from a height of 2.5 m and rebounds to a height of 1.8 m. The experiment in

Conservation of Mechanical Energy in a Roller Coaster

A roller coaster car with a mass of 500 kg is released from rest at the top of a hill of height 20 m

Conservation of Mechanical Energy on a Frictionless Incline

A $$3\;kg$$ block is released from rest at a height of $$5\;m$$ on a frictionless inclined plane. Us

Crane Lifting with Force Angle

A crane lifts a 2000 kg load vertically by 10 m using a cable that makes a 15° angle with the vertic

Determining Frictional Work on a Block on an Incline

Develop an experiment to quantify the work done by friction on a block sliding down an inclined plan

Determining Power Output in a Weightlifting Scenario

A weightlifter lifts a 100 kg weight vertically upward by 1.2 m in 2 seconds. Answer all parts.

Determining Work with Nonconservative Forces

A 3 kg block is placed on a 10 m high frictional ramp and is released from rest. It slides down the

Energy Dissipation in a Bouncing Ball

A 0.5 kg ball is dropped from a height of 5 m and subsequently bounces back to a height of 3.5 m. An

Energy Dissipation in a Collision

Analyze the experimental data from an inelastic collision that shows changes in kinetic energy befor

Energy Loss Analysis in a Braking Disk Experiment

In an experiment examining the deceleration of a spinning disk, a student applies a braking force an

Evaluating Mechanical Energy during a Bounce

Analyze the experimental data from a bouncing ball that tracks bounce height and kinetic energy at i

Evaluating Stationary Bike Power Output and Energy Expenditure

At a gym, an experiment is conducted on a stationary bike to evaluate cycling power output. The bike

Investigating Power Variations in Electric Motor-Driven Lifts

An electric motor is used to power a lift that raises a load at constant speed. The experiment recor

Investigating the Effect of Force Angle on Work Done

You are tasked with developing an experiment to study how the angle of an applied force affects the

Lifting a Dumbbell at an Angle

A person lifts a 10 kg dumbbell from the floor by applying a force at an angle of 30° above the hori

Motor Power and Efficiency

A motor lifts a 150 kg load vertically by 4 m in 10 s. The motor consumes 10,000 J of electrical ene

Nonconservative Forces and Energy Loss

A 2 kg sled slides down a hill of height $$5 m$$. Due to friction, the sled loses energy equivalent

Nonconservative Losses in an Elastic Collision Experiment

In an experiment, a student investigates energy conservation during an elastic collision between two

Pendulum Energy Transformation

A simple pendulum with a 2 m long string and a 2 kg bob is released from a 30° angle from the vertic

Power Output Variability in a Walking Robot

A walking robot performs cyclic motion. In one cycle, the robot does 150 J of work in 2 seconds. Ans

Relating Electrical and Mechanical Power in a Conveyor Belt System

An electric motor supplies an electrical power output of $$750 W$$ to a conveyor belt system and ope

Torque, Work, and Mechanical Advantage in Using a Wrench

A mechanic uses a 0.4 m long wrench to loosen a bolt. A force is applied at an angle of 60° relative

Work Done by a Variable Force

A force applied to an object varies with displacement, as shown in the provided Force vs. Displaceme

Work Done by a Variable Force

In an experiment, a cart is subjected to a variable force along its displacement. A graph of force v

Work Done in Pushing a Box on a Horizontal Surface

A person pushes a box by applying a force of $$40\,N$$ at an angle of $$20^{\circ}$$ above the horiz

Work in Uniform Circular Motion

A common claim in physics is that an object in uniform circular motion experiences a centripetal for

Work Measurement Under Non-Uniform Acceleration

In this experiment, a student measures the work done on a cart that accelerates along a track. A for

Work-Energy Theorem in Motion Analysis

A 3 kg block, initially at rest, is accelerated along a horizontal surface and reaches a speed of 8

Air Track Momentum Experiment

In an air track experiment, two gliders undergo a collision. Glider 1 (mass $$0.50\,kg$$) has an ini

Analyzing Rebounding Basketball

A basketball of mass $$0.62 \ kg$$ is dropped from a certain height. Just before impact, its speed i

Calculating Linear Momentum and Impulse

In this problem, you will calculate linear momentum and impulse for a moving object and relate impul

Collision with Energy Absorption via Spring Mechanism

A 3 kg block moving at $$10\,\text{m/s}$$ collides with a spring attached to a wall. The block compr

Comparing Elastic and Inelastic Collisions

Two objects undergo collisions under different conditions. Experiment 1 features an elastic collisio

Diver's Momentum and Water Impact

A diver with a mass of $$70 \ kg$$ jumps off a diving board with a horizontal component of velocity

Experimental Analysis of Momentum Transfer

An experiment using carts on an air track measured momentum before and after collisions to test mome

Experimental Uncertainty in Momentum Measurements

During an experiment to measure the momentum of a moving cart, various uncertainties arise in measur

Firework Launch Momentum Analysis

A researcher studies the launch of a firework rocket by measuring both force over time and the subse

Impact of External Forces on Momentum Conservation

Investigate how small external forces, such as air resistance or friction, can affect the conservati

Impulse Analysis in Variable Mass Systems

A cart moving on a frictionless track collects rainwater, causing its mass to increase over time. A

Impulse and Momentum in Baseball Bat Design

Engineers are investigating how the mass and swing speed of a baseball bat affect the impulse delive

Impulse in Variable Force Experiment

In an experiment, a student applies a variable force to a cart. The force-time graph, provided as a

Inelastic Collision: Objects Sticking Together

A 2 kg cart moving at $$8\,\text{m/s}$$ collides with a 3 kg cart moving at $$4\,\text{m/s}$$ in the

Investigating Elastic and Inelastic Collisions

In a laboratory setup, two carts are made to collide under two different conditions: one where they

Misinterpretation of Force-Time Graph in Impulse Determination

In this experiment, students used a force sensor to record data during an object’s collision and plo

Momentum and Impulse in a Robotic Arm

In a manufacturing process, a robotic arm picks up a moving object of mass $$5 \ kg$$ traveling at $

Momentum and Impulse in Circular Motion

Consider an object moving in uniform circular motion. A brief tangential force is applied, deliverin

Momentum and Kinetic Energy Distribution in Explosions

An object at rest in space explodes into two fragments: Fragment A (mass = $$4$$ kg) and Fragment B

Momentum in Frictional Collisions

A researcher investigates collisions on a rough surface, where friction affects the momentum of slid

Multi-Stage Cart Collision

Three carts are placed on a frictionless track. Cart A (1.0 kg) is moving at 4.0 m/s toward Cart B (

One-Dimensional Collision and Momentum Conservation

On a frictionless surface, Object 1 (mass = 2 kg) is moving east at 3 m/s, and Object 2 (mass = 3 kg

Recoil Momentum in Firearm Dynamics

A 7.0 kg firearm fires a 0.015 kg bullet horizontally at a speed of 400 m/s. Neglecting external for

Rocket Propulsion and Momentum Conservation

A rocket in space propels itself by ejecting fuel at a constant exhaust velocity. As the fuel is exp

Scaling of Momentum with Velocity

An object's momentum is directly proportional to its velocity. Explore the effects of changes in vel

Soccer Kick: Impulse and Momentum

A soccer player kicks a ball, applying a variable force over the period of contact. A force-versus-t

Solving for Final Momentum in a Multi-Collision System

Consider a system with three objects undergoing sequential collisions. Object A (mass = 2 kg, veloci

Traffic Safety and Momentum in Multi-Car Collisions

A traffic safety study reconstructs a multi-car collision where several vehicles collide and move to

Two-Dimensional Collision Analysis

Two hockey pucks on an air-cushioned table undergo a collision. Their initial data are provided in t

Amplitude and SHM: Effect on Oscillation

In an ideal mass-spring oscillator, the period is independent of the amplitude of oscillation. Howev

Amplitude Effects on Energy

A researcher examines how changes in amplitude affect the total mechanical energy of a mass-spring s

Beat Frequency in Coupled Oscillators

Two mass-spring oscillators, having slightly different angular frequencies, are coupled so that thei

Comparison of Pendulum and Spring Systems

Compare the factors that affect the period of oscillation in a mass-spring system versus a simple pe

Designing an SHM Experiment

Design an experiment to study the effect of varying the spring constant (k) on the period (T) of a m

Determining System Parameters from SHM Equations

A researcher is given an equation for the displacement of a mass-spring system: $$x = 0.05 \cos(25t

Determining the Impact of Air Resistance on Amplitude Decay in SHM

An experiment records the amplitude of a damped oscillator over successive cycles in the presence of

Determining the Period of a Simple Pendulum

A simple pendulum has a period given by $$T = 2\pi \sqrt{\frac{L}{g}}$$. Consider a pendulum with a

Effect of Amplitude on Energy in SHM

For a mass-spring system in simple harmonic motion, the total mechanical energy is directly related

Energy Transformation in SHM

In a mass-spring system undergoing SHM, the total mechanical energy is conserved and is partitioned

Energy Transformation in SHM

Consider a mass-spring system in SHM where at maximum displacement all energy is potential and at eq

Force Analysis in SHM

Analyze the force exerted by a spring on a mass undergoing simple harmonic motion using Hooke's law.

Impulse and SHM Initiation

Investigate how a sudden impulse initiates simple harmonic motion in a mass-spring system.

Investigating Measurement Uncertainties in SHM Experiments

A researcher conducts an experiment on a mass-spring system to measure its oscillation period, but o

Mass Variation in SHM

A series of experiments was performed using a mass-spring system with different masses. The measured

Mass-Spring Oscillator Analysis

Consider a mass on a spring undergoing SHM described by the displacement equation $$ x = A * \cos(\o

Mathematical Derivation in SHM

Derive the second-order differential equation governing the motion of a mass-spring system in SHM. A

Misapplication of Hooke's Law in Oscillatory Force Experiment

A student examines the relationship between displacement and force in a spring system. In the experi

Misinterpretation of Velocity Data in SHM Experiment

In an experiment aimed at verifying the velocity function in SHM, a student records the displacement

Misleading Data Analysis in Pendulum Length Experiment

A student performs an experiment to study the relationship between the length of a pendulum and its

Oscillatory Motion with Variable Amplitude

Explore the behavior and safety implications of a driven harmonic oscillator with variable amplitude

Pendulum Motion and Period Analysis

A simple pendulum with small oscillations obeys the period equation $$ T = 2\pi * \sqrt{\frac{L}{g}}

Pendulum Period Calculation

A simple pendulum of length $$L$$ swings under the influence of gravity $$g$$. The period of a pendu

Pendulum Period Investigation

A researcher is studying the period of a simple pendulum. The period is given by $$T = 2\pi \sqrt{\f

Period and Frequency Relationship Analysis

Examine the relationship between the period and frequency of an oscillator using the provided data.

Real-World Applications of SHM

An engineering suspension system can be modeled as a mass-spring-damper system exhibiting simple har

Simple Harmonic Motion in Biological Systems

Biological systems, such as the rhythmic beating of a heart or neuron firing patterns, sometimes exh

Testing Amplitude Independence of Period in SHM

An experiment is designed to test the hypothesis that the period of an ideal mass-spring system unde

Understanding the Effect of Spring Constant

Investigate how the spring constant $$ k $$ influences the frequency and period of oscillation in a

Analysis of Angular Velocity and Tangential Speed via Graph

A researcher examines the relationship between angular velocity and tangential speed for a point on

Angular Displacement Calculation from Non-Uniform Acceleration

A rotating object has an angular acceleration that varies with time according to the function $$\alp

Angular Displacement from Arc Length Measurements

A small robot moves along a curved path that is part of a circle with a radius of $$r = 0.5\,m$$. It

Angular Kinematics Analysis: Table Data

A researcher collected data for a rotating turntable's angular displacement over 10 s. The data are

Angular Momentum Conservation in a Collision

A rotating disk with moment of inertia $$I_d$$ and angular velocity of 5.0 rad/s collides with a sma

Center of Mass vs. Geometric Center: A Rotational Dynamics Experiment

In an experiment on a non-uniform rod, mass elements are recorded at various positions along the rod

Combined Translation and Rotation: A Rolling Ball

A solid sphere of mass $$3 \;kg$$ and radius $$0.2 \;m$$ rolls without slipping down a 30° incline.

Comparative Analysis of Rotational Motion in Different Systems

Two systems—a disc and a rod—are subjected to the same net torque. Their moments of inertia and corr

Comparative Analysis: Rotational vs. Translational Motion

Analyze the similarities and differences between the equations of translational motion (e.g., $$F_{n

Composite Object Mass Distribution and Rotational Inertia Experiment Error

A student conducts an experiment to determine the rotational inertia of a composite object made from

Compound Pendulum Period Calculation Error

A student sets up an experiment with a compound pendulum by suspending a rigid body from a pivot and

Effect of Added Mass on Moment of Inertia

In an experiment, a uniform disk is modified by attaching small point masses at its rim. The purpose

Energy Analysis of a Spinning Disc

A flat, circular disc in an industrial machine accelerates from rest to 100 rad/s in 10 seconds. Its

Energy Considerations in Rotational Motion

An experiment measures both the rotational and translational kinetic energies of a rolling object. T

Energy Considerations in Rotational Systems

Explore how changes in the moment of inertia affect the rotational kinetic energy of a system, assum

Evaluating Friction and Air Resistance Effects

Design an experiment to evaluate the effects of friction and air resistance on the rotational decele

Graphical Analysis of Angular Velocity vs. Time

A graph of angular velocity (\(\omega\)) versus time for a rotating disc is provided. Analyze the ro

Impact of Body Position on Rotational Speed in Diving

A diver alters her body position during a dive, reducing her moment of inertia. Analyze how this cha

Moment of Inertia Calculations for Simple Shapes

A thin rod of mass $$m = 2 \text{ kg}$$ and length $$L = 1.5 \text{ m}$$ is considered for rotationa

Oscillations of a Physical Pendulum

A uniform wooden rod of length 1 m oscillates as a physical pendulum about a pivot near one end. The

Relating Linear and Angular Motion

A disk rotates with an angular velocity of $$\omega = 12 \;rad/s$$ and has a radius of $$r = 0.5 \;m

Rolling Cylinder Angular Acceleration Measurement Error

A student investigates the acceleration of a rolling cylinder down an inclined plane. The experiment

Rotational Dynamics in Amusement Park Rides

An amusement park ride features a rotating swing platform with a radius of $$3.5 \;m$$ rotating at a

Rotational Kinetic Energy Calculations

Rotational kinetic energy is given by the expression $$KE_{rot} = 0.5 * I * \omega^2$$. For a disc w

Rotational Motion in a Laboratory Experiment

A rotating object's angular velocity was recorded over time in a laboratory experiment. The followin

Spinning Bicycle Wheel Damping Experiment Error

A student investigates the deceleration of a spinning bicycle wheel by measuring its angular velocit

Torque Analysis on a Rotating Lever

A rigid lever pivots about one end. Forces are applied perpendicularly at various distances from the