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

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Question: A wheel of radius R is rolling without slipping on a horizontal surface. What is the relationship between the linear velocity v of the center of the wheel and its angular velocity ω?

Options:

  1. v = Rω
  2. v = ω/R
  3. v = 2Rω
  4. v = ω/2R

Correct Answer: v = Rω

Solution: 

For rolling without slipping, the linear velocity v is related to angular velocity ω by the equation v = Rω.

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

Practice Questions

Q1
A wheel of radius R is rolling without slipping on a horizontal surface. What is the relationship between the linear velocity v of the center of the wheel and its angular velocity ω?
  1. v = Rω
  2. v = ω/R
  3. v = 2Rω
  4. v = ω/2R

Questions & Step-by-Step Solutions

A wheel of radius R is rolling without slipping on a horizontal surface. What is the relationship between the linear velocity v of the center of the wheel and its angular velocity ω?
  • Step 1: Understand that the wheel is rolling without slipping, which means the point of contact between the wheel and the ground is not sliding.
  • Step 2: Recognize that the wheel has a radius R, which is the distance from the center of the wheel to the edge.
  • Step 3: Know that the linear velocity v is the speed of the center of the wheel moving forward.
  • Step 4: Understand that the angular velocity ω is how fast the wheel is spinning around its center.
  • Step 5: Realize that when the wheel rolls without slipping, the distance it rolls forward (linear distance) is equal to the distance it rotates (circumference of the wheel).
  • Step 6: The circumference of the wheel is given by the formula 2πR. This is the distance the wheel covers in one complete rotation.
  • Step 7: Since the wheel rolls without slipping, the linear distance covered in one rotation (which is v) must equal the circumference (2πR) divided by the time it takes to complete one rotation.
  • Step 8: The relationship between linear velocity v and angular velocity ω can be expressed as v = Rω, where ω is the angular velocity in radians per second.
  • Rolling Motion – The relationship between linear and angular velocity for objects rolling without slipping.
  • Kinematics – Understanding the motion of objects in terms of their velocities and accelerations.
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