A disk rotates about its axis with an angular velocity of ω. If its radius is doubled while keeping the mass constant, what will be the new angular momentum?
Practice Questions
1 question
Q1
A disk rotates about its axis with an angular velocity of ω. If its radius is doubled while keeping the mass constant, what will be the new angular momentum?
2Iω
4Iω
Iω
I(2ω)
The moment of inertia I of a disk is proportional to r^2, so if the radius is doubled, I becomes 4I. Thus, angular momentum L = Iω becomes 4Iω.
Questions & Step-by-step Solutions
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Q
Q: A disk rotates about its axis with an angular velocity of ω. If its radius is doubled while keeping the mass constant, what will be the new angular momentum?
Solution: The moment of inertia I of a disk is proportional to r^2, so if the radius is doubled, I becomes 4I. Thus, angular momentum L = Iω becomes 4Iω.
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: Know that the moment of inertia (I) for a disk is proportional to the square of its radius (r). This means if the radius is doubled (2r), the new moment of inertia becomes I' = 4I (since (2r)^2 = 4r^2).
Step 3: Since the mass of the disk remains constant, we only need to consider the change in radius affecting the moment of inertia.
Step 4: Substitute the new moment of inertia into the angular momentum formula: L' = I'ω = 4Iω.
Step 5: Conclude that the new angular momentum is 4 times the original angular momentum.
