Rotational Dynamics Formulas to Know for AP Physics C: Mechanics (2025)

Torque (τ)

The rotational counterpart of force; measures how effectively a force causes an object to rotate about a pivot or axis.

Angular Acceleration (α)

The rate at which an object’s rotational speed changes; indicates how quickly an object speeds up or slows down.

Moment of Inertia (I)

A measure of an object’s resistance to changes in its rotational motion, depending on mass distribution.

Effect of Mass on Moment of Inertia

Objects with mass farther from the axis have a higher moment of inertia, making them harder to spin.

Angular Momentum (L)

A conserved quantity representing the amount of rotational motion an object has.

Conservation of Angular Momentum

States that total angular momentum remains constant if no external torque acts on a system.

Rotational Kinetic Energy (KE)

The energy an object has due to its rotation, similar to translational kinetic energy.

Combined Motion Energy

Objects in combined motion have both rotational and translational kinetic energy.

Work-Energy Theorem for Rotation

The work done by torque on a rotating object results in a change in its rotational kinetic energy.

Power in Rotational Motion (P)

Measures the rate at which work is done or energy is transferred in a rotating object.

Angular Velocity (ω)

Describes how fast an object is rotating, measured in radians per second.

Angular Displacement (θ)

The angle an object rotates through over time.

Right-Hand Rule

A method to determine the direction of torque as either clockwise or counterclockwise.

Lever Arm (r)

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

Angular Acceleration Dependence

Increasing torque leads to an increase in angular acceleration for an object.

Moment of Inertia for Common Shapes

Each object has a specific moment of inertia depending on its mass distribution.

Applications of Angular Momentum

Used in figure skating and understanding neutron stars (pulsars) in astronomy.

Rotational Kinetic Energy Formula

Kinetic energy associated with the rotation of an object.

Power Transfer Importance

Critical in systems where rotation drives power transfer, such as engines and turbines.

Angular Velocity Sign Convention

Positive omega indicates counterclockwise rotation; negative omega indicates clockwise rotation.

Angular Displacement in Motion Analysis

Used to analyze motion under constant angular acceleration.

Energy Conservation in Wind Turbines

Wind turbines convert rotational energy into electrical energy.

Torque Formula

Equation describing how torque is calculated based on force, distance, and angle.

Angular Momentum Conservation Equation

Mathematical representation of the conservation of angular momentum principle.

Kinetic Energy Comparison

Comparison of rotational and translational kinetic energy in moving objects.

Power Formula in Rotation

Formula that defines how power is calculated in rotational motion.

Angular Acceleration Formula

Mathematical representation of how angular acceleration relates to torque and moment of inertia.

Angular Position Over Time

How the angle of rotation changes as a function of time.

Rotational System Power Measurement

Quantifies the efficiency and output of devices relying on rotational motion.

Key Factors in Rotational Dynamics

Torque, angular acceleration, moment of inertia, and angular momentum are core to understanding rotation.