A rotating object has an angular momentum of 12 kg·m²/s and a moment of inertia

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Question: A rotating object has an angular momentum of 12 kg·m²/s and a moment of inertia of 4 kg·m². What is its angular velocity?

Options:

Correct Answer: 3 rad/s

Solution:

Angular momentum L = Iω, thus ω = L/I = 12 kg·m²/s / 4 kg·m² = 3 rad/s.

A rotating object has an angular momentum of 12 kg·m²/s and a moment of inertia of 4 kg·m². What is its angular velocity?

A rotating object has an angular momentum of 12 kg·m²/s and a moment of inertia of 4 kg·m². What is its angular velocity?

Correct Answer: 3 rad/s

Step 1: Understand the formula for angular momentum, which is L = Iω, where L is angular momentum, I is moment of inertia, and ω is angular velocity.
Step 2: Identify the values given in the question: L (angular momentum) is 12 kg·m²/s and I (moment of inertia) is 4 kg·m².
Step 3: Rearrange the formula to solve for angular velocity (ω): ω = L/I.
Step 4: Substitute the values into the formula: ω = 12 kg·m²/s / 4 kg·m².
Step 5: Perform the division: 12 divided by 4 equals 3.
Step 6: Conclude that the angular velocity (ω) is 3 rad/s.

Angular Momentum – Angular momentum (L) is the product of a rotating object's moment of inertia (I) and its angular velocity (ω).
Moment of Inertia – Moment of inertia (I) is a measure of an object's resistance to changes in its rotation.
Angular Velocity – Angular velocity (ω) is the rate of rotation of an object, typically measured in radians per second.