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If the radius of a rotating disc is doubled while keeping the mass constant, how

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Question: 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?

Options:

  1. It doubles
  2. It remains the same
  3. It quadruples
  4. It halves

Correct Answer: It quadruples

Solution: 

Angular momentum L = Iω; if radius is doubled, moment of inertia I increases by a factor of 4, hence L quadruples.

If the radius of a rotating disc is doubled while keeping the mass constant, how

Practice Questions

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?
  1. It doubles
  2. It remains the same
  3. It quadruples
  4. It halves

Questions & Step-by-Step Solutions

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?
Correct Answer: L quadruples.
  • 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.
  • Angular Momentum – Angular momentum (L) is the product of the moment of inertia (I) and angular velocity (ω).
  • Moment of Inertia – Moment of inertia (I) depends on the mass distribution relative to the axis of rotation; for a disc, it increases with the square of the radius.
  • Conservation of Angular Momentum – Angular momentum is conserved in a closed system unless acted upon by an external torque.
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