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A rotating object has an angular momentum of 12 kg·m²/s and a moment of inertia
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?
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Practice Questions
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Q1
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?
3 rad/s
4 rad/s
2 rad/s
1 rad/s
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Angular momentum L = Iω, thus ω = L/I = 12 kg·m²/s / 4 kg·m² = 3 rad/s.
Questions & Step-by-step Solutions
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Q
Q: 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?
Solution:
Angular momentum L = Iω, thus ω = L/I = 12 kg·m²/s / 4 kg·m² = 3 rad/s.
Steps: 6
Show Steps
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.
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