In a rotating system, if the angular momentum is doubled while the moment of inertia remains constant, what happens to the angular velocity?

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Q: In a rotating system, if the angular momentum is doubled while the moment of inertia remains constant, what happens to the angular velocity?

Solution: Since L = Iω, if L is doubled and I remains constant, then 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 problem, the moment of inertia (I) remains constant.
Step 3: Recognize that if the angular momentum (L) is doubled, we can express this as 2L.
Step 4: Set up the equation with the new angular momentum: 2L = Iω'. Here, ω' is the new angular velocity we want to find.
Step 5: Since L = Iω, we can replace L in the equation: 2(Iω) = Iω'.
Step 6: Simplify the equation: 2Iω = Iω'.
Step 7: Since I is constant and not zero, we can divide both sides by I: 2ω = ω'.
Step 8: This shows that the new angular velocity (ω') is double the original angular velocity (ω).