A rotating object has an angular momentum L. If the moment of inertia of the object is doubled while keeping the angular velocity constant, what happens to the angular momentum?
Practice Questions
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Q1
A rotating object has an angular momentum L. If the moment of inertia of the object is doubled while keeping the angular velocity constant, what happens to the angular momentum?
It doubles
It halves
It remains the same
It quadruples
Angular momentum L = Iω. If I is doubled and ω remains constant, L also doubles.
Questions & Step-by-step Solutions
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Q
Q: A rotating object has an angular momentum L. If the moment of inertia of the object is doubled while keeping the angular velocity constant, what happens to the angular momentum?
Solution: Angular momentum L = Iω. If I is doubled and ω remains constant, L also doubles.
Steps: 6
Step 1: Understand that angular momentum (L) is calculated using the formula L = Iω, where I is the moment of inertia and ω is the angular velocity.
Step 2: Identify that in this scenario, the moment of inertia (I) is being doubled. This means if the original moment of inertia is I, the new moment of inertia will be 2I.
Step 3: Note that the angular velocity (ω) remains constant, meaning it does not change.
Step 4: Substitute the new moment of inertia into the angular momentum formula: L = (2I)ω.
Step 5: Compare the new angular momentum (L) with the original angular momentum. Since L = Iω originally, the new angular momentum becomes L = 2(Iω).
Step 6: Conclude that since the new angular momentum is 2 times the original angular momentum, the angular momentum doubles.
