AP Physics 1: Rotational Dynamics & Newton's Laws

Rotational Motion

Objects spinning around an axis.

Torque

A force that causes angular acceleration.

Rotational Equilibrium

Occurs when the net torque acting on a system is zero.

Angular acceleration ($\alpha$)

The rate of change of angular velocity.

Complete Static Equilibrium

Condition when both translational and rotational equilibrium are met simultaneously.

Translational Equilibrium

The state where the net force on an object is zero.

Net Torque ($\sum \tau$)

The vector sum of all torques acting on an object.

Moment of Inertia ($I$)

The measure of an object's resistance to changes in its rotational motion.

Angular Velocity ($\omega$)

The rate at which an object rotates around an axis.

Friction in Rolling Motion

Static friction is necessary for an object to rotate while rolling.

Newton's Second Law (Rotational Form)

$\sum \tau = I\alpha$ relates torque, moment of inertia, and angular acceleration.

Pivot Point

The point about which an object rotates; used in torque calculations.

Counter-Clockwise (CCW)

The direction considered positive in torque calculations.

Lever Arm

The perpendicular distance from the axis of rotation to the line of action of the force.

Uniform Board

A board with a constant mass distribution, affecting moments of inertia.

Torque from Weight

Torque calculated using \tau = r \cdot mg where $mg$ is the force of gravity.

Condition for Rolling

Static friction must act at the point of contact for an object to roll.

Pulley Dynamics

A situation where rotational motion of a pulley affects linear motion of a hanging mass.

Analogous Concepts

Comparing linear dynamics (e.g., force) to rotational dynamics (e.g., torque).

Rolling Without Slipping

Condition where a rolling object does not slide, adhering to kinematic relationships.

Inertia Comparison

Comparing how mass distribution affects the moment of inertia of different shapes.

Sign Convention

Standard agreement on signs (positive/negative) for torques during calculations.

Equilibrium Conditions

Both net force and net torque must be zero for an object to be in equilibrium.

Energy Conversion in Rolling Objects

Potential energy is converted into both translational and rotational kinetic energy.

Common Mistakes in Torque Problems

Errors typically made include not defining pivot points or mixing linear and rotational concepts.

Formula for Moment of Inertia of a Solid Cylinder

I = \frac{1}{2}MR^2, where $M$ is mass and $R$ is radius.

Seesaw Balance Problem

A scenario involving two masses balanced on a fulcrum requiring torque analysis.