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A wheel of radius R rolls without slipping on a horizontal surface. If it rotate

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Question: A wheel of radius R rolls without slipping on a horizontal surface. If it rotates with an angular velocity ω, what is the linear velocity of the center of the wheel?

Options:

  1. Rω
  2. 2Rω
  3. ω/R
  4. R/ω

Correct Answer: Rω

Solution: 

The linear velocity v of the center of the wheel is related to the angular velocity ω by the equation v = Rω.

A wheel of radius R rolls without slipping on a horizontal surface. If it rotate

Practice Questions

Q1
A wheel of radius R rolls without slipping on a horizontal surface. If it rotates with an angular velocity ω, what is the linear velocity of the center of the wheel?
  1. Rω
  2. 2Rω
  3. ω/R
  4. R/ω

Questions & Step-by-Step Solutions

A wheel of radius R rolls without slipping on a horizontal surface. If it rotates with an angular velocity ω, what is the linear velocity of the center of the wheel?
  • Step 1: Understand that the wheel is rolling without slipping, which means the point of contact with the ground is not sliding.
  • Step 2: Recall that the angular velocity (ω) tells us how fast the wheel is spinning around its center.
  • Step 3: Recognize that the radius (R) of the wheel is the distance from the center of the wheel to the edge.
  • Step 4: Realize that the linear velocity (v) of the center of the wheel is how fast the center is moving in a straight line.
  • Step 5: Use the relationship between linear velocity and angular velocity, which is given by the formula v = Rω.
  • Step 6: Substitute the values of R and ω into the formula to find the linear velocity v.
  • Relationship between Angular and Linear Velocity – The linear velocity of a point on a rotating object is directly proportional to its angular velocity and the radius of the rotation.
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