Rotation & Angular Dynamics · Physics

Torque drives angular acceleration through inertia.

Rotational dynamics is Newton’s second law in angular form. Net torque sets angular acceleration, and the moment of inertia tells how strongly a body resists rotational change.

This topic

Rotational Dynamics (τ = Iα)

Learn the rotational version of F = ma, then apply it to real rigid bodies and torque balances.

Core law

Newton’s second law for rotation

For rotation about a fixed axis, net torque plays the role of net force, and angular acceleration plays the role of linear acceleration.

Statement: Στ = Iα (fixed axis)
Direction and sign conventions matter
What counts as “net torque” about a chosen axis
When “fixed axis” is a good model

Inertia

Moment of inertia as rotational mass

Moment of inertia tells how mass is distributed relative to an axis. The same object can have different I values about different axes.

I depends on axis choice, not just shape
Mass farther from the axis increases I strongly
Units: kg·m²
Using standard I values vs computing from definition

Application

Applying τ = Iα to rigid bodies

Once you can compute torque and identify I about the correct axis, τ = Iα becomes a direct tool for predicting angular acceleration and angular speed changes.

Identify torques that accelerate vs oppose motion
Relate angular results to linear quantities at a radius
Common setups: pulleys, disks, rods about pivots
Check limiting cases (large I → small α)

Connection

Comparison with F = ma

Translational and rotational dynamics mirror each other. Mapping the “roles” helps you reason quickly and check whether an equation makes sense.

Force ↔ torque
Mass ↔ moment of inertia
Linear acceleration ↔ angular acceleration
Work/energy parallels later in the track

Practice

Practice & Exercises

Practice building torque balances, choosing the correct I, and solving for α, ω, and related linear quantities.

Compute Στ about a chosen axis (signs)
Use τ = Iα in disk/rod/pulley scenarios
Translate angular results into v and a at a radius
Check assumptions (fixed axis, rigid body)
Exam-style rotational dynamics sets