An object has rotational inertia I. The object, initially at rest, begins to rotate with a constant angular acceleration of magnitude α. What is the magnitude of the angular momentum L of the object after time t? Express your answer in terms of I, α, and t.

initial angular velocity, ωo = 0

angular acceleration = α

time = t

let the angular velocity after time t is ω.

Use first equation of motion for rotational motion

ω = o + α t

ω = αt

The angular momentum is given by

Angular momentum = moment of inertia x angular velocity

L = I x ω

L = I x αt

L = I α t