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

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

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 is halved.

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

Practice Questions

Q1
If the radius of a rotating wheel is halved while keeping the angular velocity constant, what happens to the linear velocity of a point on the edge of the wheel?
  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 wheel is halved while keeping the angular velocity constant, what happens to the linear velocity of a point on the edge of the wheel?
Correct Answer: Linear velocity is halved.
  • Step 1: Understand that the linear velocity (v) of a point on the edge of a wheel is calculated using the formula v = rω, where r is the radius and ω is the angular velocity.
  • Step 2: Note that in this scenario, the radius (r) of the wheel is being halved. This means if the original radius was r, the new radius will be r/2.
  • Step 3: Recognize 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: Since (r/2)ω is half of rω, the new linear velocity is half of the original linear velocity.
  • Linear Velocity and Angular Velocity Relationship – The relationship between linear velocity (v), radius (r), and angular velocity (ω) is given by the formula v = rω. This concept tests understanding of how changes in radius affect linear velocity when angular velocity is constant.
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