A rotating wheel has an angular momentum of L. If the wheel's angular velocity is doubled, what happens to its angular momentum?

1 question

1 item

Q: A rotating wheel has an angular momentum of L. If the wheel's angular velocity is doubled, what happens to its angular momentum?

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

Steps: 5

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, we can express this as 2ω.
Step 3: Substitute the new angular velocity into the angular momentum formula: L = I(2ω).
Step 4: Simplify the equation: L = 2Iω, which means the new angular momentum is 2 times the original angular momentum (2L).
Step 5: However, since the moment of inertia (I) is also affected by the change in angular velocity, we need to consider that the new angular momentum becomes L = I(2ω) = 4L, because I remains constant and we have doubled ω.