Question

Linear acceleration is determined by the ratio of the net force on an object to the mass of the object. Based on this exploration, do you think there is a similar ratio that determines the angular acceleration of a rotating object?

Answer 1

Oh for sure. Yes. Uh huh. You bet. Definitely. There's no doubt in my mind.

The angular acceleration of a rotating object is determined by the ratio of the net torque on the object to the object's moment of inertia.

Answer 2

Recalling for motion of a body in one spatial dimension:

F = ma

F is the net force acting on the body

m is the body's mass

a is the body's acceleration

We have a very similar equation describing rotational motion:

τ = Iα

τ is the net torque (rotation force) acting on the body

I is the body's moment of inertia (around an arbitrary point), also known as rotational inertia

α is the body's angular acceleration

Rearranging the above equation gives a formula for α:

α = τ/I