A disk rotates about its axis with an angular velocity of ω. If its radius is doubled, what will be the new angular momentum if the mass remains the same?
Practice Questions
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Q1
A disk rotates about its axis with an angular velocity of ω. If its radius is doubled, what will be the new angular momentum if the mass remains the same?
2ω
4ω
ω
ω/2
Angular momentum L = Iω. If the radius is doubled, the moment of inertia increases by a factor of 4, thus L = 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, what will be the new angular momentum if the mass remains the same?
Solution: Angular momentum L = Iω. If the radius is doubled, the moment of inertia increases by a factor of 4, thus L = 4Iω.
Steps: 6
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: Recognize that the moment of inertia (I) for a disk is given by the formula I = (1/2) * m * r^2, where m is the mass and r is the radius.
Step 3: If the radius (r) is doubled, the new radius becomes 2r.
Step 4: Calculate the new moment of inertia with the new radius: I_new = (1/2) * m * (2r)^2 = (1/2) * m * 4r^2 = 4 * (1/2) * m * r^2 = 4I.
Step 5: Since the angular velocity (ω) remains the same, substitute the new moment of inertia into the angular momentum formula: L_new = I_new * ω = 4I * ω.
Step 6: Conclude that the new angular momentum is L_new = 4L, where L is the original angular momentum.
