If the moment of inertia of a body is doubled, what will happen to its angular momentum if the angular velocity remains constant?

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Q: If the moment of inertia of a body is doubled, what will happen to its angular momentum if the angular velocity remains constant?

Solution: Angular momentum L = Iω; if I is doubled and ω remains constant, L also doubles.

Steps: 7

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 that in this question, the moment of inertia (I) is being doubled.
Step 3: Note that the angular velocity (ω) remains constant, meaning it does not change.
Step 4: Since I is doubled, we can express this as I' = 2I, where I' is the new moment of inertia.
Step 5: Substitute the new moment of inertia into the angular momentum formula: L' = I'ω = (2I)ω.
Step 6: Simplify the equation: L' = 2(Iω) = 2L, where L is the original angular momentum.
Step 7: Conclude that if the moment of inertia is doubled and angular velocity remains constant, the angular momentum also doubles.