A rotating object has an angular momentum of L. If its moment of inertia is halved and the angular velocity is doubled, what is the new angular momentum?
Practice Questions
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Q1
A rotating object has an angular momentum of L. If its moment of inertia is halved and the angular velocity is doubled, what is the new angular momentum?
L
2L
4L
L/2
New angular momentum L' = I'ω' = (1/2 I)(2ω) = Iω = L.
Questions & Step-by-step Solutions
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Q
Q: A rotating object has an angular momentum of L. If its moment of inertia is halved and the angular velocity is doubled, what is the new angular momentum?
Solution: New angular momentum L' = I'ω' = (1/2 I)(2ω) = Iω = L.
Steps: 7
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 the initial angular momentum, which is given as L.
Step 3: Note that the moment of inertia (I) is halved, so the new moment of inertia (I') is I' = 1/2 I.
Step 4: Recognize that the angular velocity (ω) is doubled, so the new angular velocity (ω') is ω' = 2ω.
Step 5: Substitute the new values into the angular momentum formula: L' = I'ω' = (1/2 I)(2ω).
Step 6: Simplify the equation: L' = (1/2)(2)(Iω) = Iω.
Step 7: Since Iω is the original angular momentum L, we find that L' = L.
