If the radius of a rotating disc is doubled while keeping the mass constant, how does the angular momentum change if the angular velocity remains the same?
Practice Questions
1 question
Q1
If the radius of a rotating disc is doubled while keeping the mass constant, how does the angular momentum change if the angular velocity remains the same?
It doubles
It remains the same
It quadruples
It halves
Angular momentum L = Iω; if radius is doubled, moment of inertia I increases by a factor of 4, hence L quadruples.
Questions & Step-by-step Solutions
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Q
Q: If the radius of a rotating disc is doubled while keeping the mass constant, how does the angular momentum change if the angular velocity remains the same?
Solution: Angular momentum L = Iω; if radius is doubled, moment of inertia I increases by a factor of 4, hence L quadruples.
Steps: 7
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: Recognize that the moment of inertia (I) for a disc is calculated using the formula I = (1/2) m r^2, where m is mass and r is radius.
Step 3: If the radius (r) of the disc is doubled, the new radius becomes 2r.
Step 4: Substitute the new radius into the moment of inertia formula: I_new = (1/2) m (2r)^2 = (1/2) m (4r^2) = 2m r^2.
Step 5: Notice that the new moment of inertia (I_new) is 4 times the original moment of inertia (I_original) because I_original = (1/2) m r^2.
Step 6: Since the angular velocity (ω) remains the same, we can now calculate the new angular momentum: L_new = I_new * ω = 4 * I_original * ω.
Step 7: Conclude that the new angular momentum (L_new) is 4 times the original angular momentum (L_original), meaning it quadruples.
