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.

Explanation:

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

The angular momentum of the object in terms of angular velocity, time of motion and angular acceleration is L = Iαt.

The given parameters;

The final angular velocity of the object is determined using first kinematic equation;

The angular momentum of the object is calculated as;

Thus, the angular momentum of the object in terms of angular velocity, time of motion and angular acceleration is L = Iαt.

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