Newton's second law for rotation

Intermediate

Net torque equals I times α.

Key relationτ = Iα

The net torque equals Iα. The larger the I, the smaller the angular acceleration for a given torque.

Worked example

10 N·m on a 2 kg·m² wheel: 5 rad/s².

Common mistake

Torque and I must be about the same axis.

In more detail

Newton's second law for rotation states that the net torque equals the moment of inertia times the angular acceleration, τ = Iα, about a fixed axis.

Designing motors to deliver enough torque to spin a heavy wheel up to speed.
Calculating braking torque needed to stop a rotating machine in a set time.
A motor drives a heavy shaft and the designer uses τ = Iα to find the torque needed for a given acceleration.

Is τ = Iα the same as F = ma?

Yes, it is the rotational equivalent, with torque replacing force and moment of inertia replacing mass.

Does it apply to any axis?

For a fixed axis or the centre of mass, yes. Other cases need extra terms.

Is this the rotational version of F = ma?

Yes. Torque plays the role of force, moment of inertia the role of mass, and angular acceleration the role of acceleration.