5.2 Angular Acceleration

What is angular acceleration?

Angular acceleration (α) is the rate of change of angular velocity (ω) over time: α = Δω/Δt, measured in rad/s². It's the rotational analog of linear acceleration. A net torque acting on an object causes it to have angular acceleration, just as a net force causes linear acceleration.

Newton's Second Law for rotation

The rotational form of Newton's Second Law is τ_net = Iα, where τ_net is net torque, I is rotational inertia (moment of inertia), and α is angular acceleration. Larger rotational inertia means a given torque produces smaller angular acceleration — objects with mass farther from the axis resist angular acceleration more.

Linking angular and linear quantities

For a point at radius r from the rotation axis, tangential (linear) acceleration a_t = rα. This connects rotational kinematics to linear motion of points on a rotating rigid body. Angular acceleration is constant when net torque and rotational inertia are constant, allowing use of rotational kinematic equations analogous to linear ones.

Key terms

Angular acceleration (α)

The rate of change of angular velocity over time: α = Δω/Δt, measured in rad/s².

Rotational form of Newton's Second Law

τ_net = Iα — net torque equals rotational inertia times angular acceleration.

Rotational inertia (I)

A measure of an object's resistance to angular acceleration; depends on mass distribution relative to the axis.

Tangential acceleration formula

a_t = rα — tangential acceleration of a point equals its radius times the angular acceleration.

What causes angular acceleration?

A net torque acting on an object, analogous to how net force causes linear acceleration.

Try an AP-style question

A wheel speeds up from rest to 20 rad/s in 4 s. What is its angular acceleration?

1. 80 rad/s²
2. 5 rad/s²
3. 20 rad/s²
4. 0.2 rad/s²