A rotating object has an angular momentum of L. If its angular velocity is doubled and its moment of inertia remains constant, what will be the new angular momentum?
Practice Questions
1 question
Q1
A rotating object has an angular momentum of L. If its angular velocity is doubled and its moment of inertia remains constant, what will be the new angular momentum?
L
2L
4L
L/2
Angular momentum L = Iω, if ω is doubled, L becomes 2I(2ω) = 4L.
Questions & Step-by-step Solutions
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Q
Q: A rotating object has an angular momentum of L. If its angular velocity is doubled and its moment of inertia remains constant, what will be the new angular momentum?
Solution: Angular momentum L = Iω, if ω is doubled, L becomes 2I(2ω) = 4L.
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: Note that in this problem, the moment of inertia (I) remains constant.
Step 3: Recognize that if the angular velocity (ω) is doubled, it becomes 2ω.
Step 4: Substitute the new angular velocity into the angular momentum formula: L = I(2ω).
Step 5: Simplify the equation: L = 2Iω.
Step 6: Since the original angular momentum is L = Iω, we can express the new angular momentum as L' = 2L.
Step 7: Therefore, if we double the angular velocity, the new angular momentum becomes 4L.
