If the angular momentum of a rotating object is doubled while its moment of inertia remains constant, what happens to its angular velocity?

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Q: If the angular momentum of a rotating object is doubled while its moment of inertia remains constant, what happens to its angular velocity?

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

Steps: 8

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 scenario, the moment of inertia (I) remains constant.
Step 3: Recognize that if the angular momentum (L) is doubled, we can express this as 2L = Iω'.
Step 4: Since I is constant, we can set up the equation: 2L = Iω' and L = Iω.
Step 5: Substitute L from the second equation into the first: 2(Iω) = Iω'.
Step 6: Simplify the equation: 2Iω = Iω'.
Step 7: Since I is constant and can be divided out, we get 2ω = ω'.
Step 8: This means that the new angular velocity (ω') is double the original angular velocity (ω).