Question: If a rotating object has an angular momentum of 20 kg·m²/s and a moment of inertia of 4 kg·m², what is its angular velocity?
Options:
2 rad/s
5 rad/s
10 rad/s
15 rad/s
Correct Answer: 5 rad/s
Solution:
Using L = Iω, we find ω = L/I = 20 kg·m²/s / 4 kg·m² = 5 rad/s.
If a rotating object has an angular momentum of 20 kg·m²/s and a moment of inert
Practice Questions
Q1
If a rotating object has an angular momentum of 20 kg·m²/s and a moment of inertia of 4 kg·m², what is its angular velocity?
2 rad/s
5 rad/s
10 rad/s
15 rad/s
Questions & Step-by-Step Solutions
If a rotating object has an angular momentum of 20 kg·m²/s and a moment of inertia of 4 kg·m², what is its angular velocity?
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 20 kg·m²/s and I (moment of inertia) is 4 kg·m².
Step 3: Rearrange the formula to solve for angular velocity (ω). The rearranged formula is ω = L/I.
Step 4: Substitute the values into the rearranged formula: ω = 20 kg·m²/s / 4 kg·m².
Step 5: Perform the division: 20 divided by 4 equals 5.
Step 6: Conclude that the angular velocity (ω) is 5 rad/s.
Angular Momentum – Angular momentum (L) is the product of moment of inertia (I) and angular velocity (ω), represented by the formula L = Iω.
Moment of Inertia – Moment of inertia (I) is a measure of an object's resistance to changes in its rotation, depending on the mass distribution relative to the axis of rotation.
Angular Velocity – Angular velocity (ω) is the rate of rotation of an object, typically measured in radians per second.
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