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

Solution: Angular momentum L = Iω, if ω is doubled, L becomes 2I(2ω) = 4L.

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 if the angular velocity (ω) is doubled, it becomes 2ω.
Step 3: Substitute the new angular velocity into the angular momentum formula: L = I(2ω).
Step 4: Rewrite the equation: L = 2Iω.
Step 5: Notice that the original angular momentum was L = Iω, so we can replace Iω with L in the new equation: L = 2L.
Step 6: Realize that the moment of inertia (I) does not change, so we can also express the new angular momentum as L = 4L, since we have doubled the angular velocity.