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If the radius of a rotating object is halved while keeping the angular velocity

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Question: If the radius of a rotating object is halved while keeping the angular velocity constant, what happens to the linear velocity at the edge?

Options:

  1. It doubles
  2. It halves
  3. It remains the same
  4. It becomes zero

Correct Answer: It halves

Solution: 

Linear velocity v = rω. If r is halved and ω remains constant, v also halves.

If the radius of a rotating object is halved while keeping the angular velocity

Practice Questions

Q1
If the radius of a rotating object is halved while keeping the angular velocity constant, what happens to the linear velocity at the edge?
  1. It doubles
  2. It halves
  3. It remains the same
  4. It becomes zero

Questions & Step-by-Step Solutions

If the radius of a rotating object is halved while keeping the angular velocity constant, what happens to the linear velocity at the edge?
Correct Answer: Linear velocity bhi half ho jayegi.
  • Step 1: Understand the formula for linear velocity, which is v = rω, where v is linear velocity, r is radius, and ω is angular velocity.
  • Step 2: Identify that in this scenario, the radius (r) is being halved. This means if the original radius is r, the new radius will be r/2.
  • Step 3: Note that the angular velocity (ω) remains constant, meaning it does not change.
  • Step 4: Substitute the new radius into the formula: v = (r/2)ω.
  • Step 5: Compare the new linear velocity with the original: The original linear velocity was v = rω, and the new linear velocity is v = (r/2)ω.
  • Step 6: Realize that (r/2)ω is half of rω, so the new linear velocity is half of the original linear velocity.
  • Step 7: Conclude that if the radius is halved while keeping angular velocity constant, the linear velocity at the edge also halves.
  • Linear Velocity and Angular Velocity Relationship – The linear velocity of a point on a rotating object is directly proportional to the radius and the angular velocity, expressed as v = rω.
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