Question

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.

Answer 1

Answer:

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

Answer 2

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

The given parameters;

• Rotational inertia of the object,  = I
• Initial angular velocity of the object, ω₀ = 0
• Angular acceleration of the object, = α
• Angular momentum of the object, = L
• Time of motion of the object, = t

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

$\omega_f = \omega_i + \alpha t\\\\\omega_f = 0 + \alpha t\\\\\omega_f = \alpha t$

The angular momentum of the object is calculated as;

$L= I\omega_f$

$L = I\alpha t$

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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