A rotating wheel has an angular momentum of L. If the wheel's angular velocity is doubled, what will be the new angular momentum?

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Q: A rotating wheel has an angular momentum of L. If the wheel's angular velocity is doubled, what will be the new angular momentum?

Solution: Angular momentum L is proportional to angular velocity, so if angular velocity is doubled, angular momentum becomes 4L.

Steps: 5

Step 1: Understand that angular momentum (L) is related to angular velocity (ω). The formula for angular momentum is L = I * ω, where I is the moment of inertia.
Step 2: Recognize that if the angular velocity (ω) is doubled, we can express this as ω' = 2ω, where ω' is the new angular velocity.
Step 3: Substitute the new angular velocity into the angular momentum formula: L' = I * ω' = I * (2ω).
Step 4: Simplify the equation: L' = 2 * (I * ω) = 2L, which shows that angular momentum is now twice the original value.
Step 5: However, since angular momentum is proportional to the square of the angular velocity, if we double the angular velocity, the angular momentum actually becomes 4 times the original: L' = 4L.