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A wheel of radius R is rolling without slipping on a horizontal surface. If the

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Question: A wheel of radius R is rolling without slipping on a horizontal surface. If the wheel has an angular velocity ω, what is the linear velocity of the center of the wheel? (2023)

Options:

  1. Rω
  2. ω/R
  3. ω
  4. 2Rω

Correct Answer: Rω

Exam Year: 2023

Solution: 

The linear velocity v of the center of the wheel is given by v = Rω.

A wheel of radius R is rolling without slipping on a horizontal surface. If the

Practice Questions

Q1
A wheel of radius R is rolling without slipping on a horizontal surface. If the wheel has an angular velocity ω, what is the linear velocity of the center of the wheel? (2023)
  1. Rω
  2. ω/R
  3. ω
  4. 2Rω

Questions & Step-by-Step Solutions

A wheel of radius R is rolling without slipping on a horizontal surface. If the wheel has an angular velocity ω, what is the linear velocity of the center of the wheel? (2023)
  • 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 the relationship between angular velocity (ω) and linear velocity (v) for a rolling object.
  • Step 3: Remember that the linear velocity (v) of the center of the wheel is directly related to the radius (R) of the wheel and its angular velocity (ω).
  • Step 4: Use the formula v = Rω to find the linear velocity of the center of the wheel.
  • 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 rotation.
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