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A disk rolls without slipping on a horizontal surface. If its radius is R and it

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Question: A disk rolls without slipping on a horizontal surface. If its radius is R and it rolls with a linear speed v, what is the angular speed of the disk?

Options:

  1. v/R
  2. R/v
  3. vR
  4. v^2/R

Correct Answer: v/R

Solution: 

The relationship between linear speed and angular speed for rolling without slipping is given by Ο‰ = v/R.

A disk rolls without slipping on a horizontal surface. If its radius is R and it

Practice Questions

Q1
A disk rolls without slipping on a horizontal surface. If its radius is R and it rolls with a linear speed v, what is the angular speed of the disk?
  1. v/R
  2. R/v
  3. vR
  4. v^2/R

Questions & Step-by-Step Solutions

A disk rolls without slipping on a horizontal surface. If its radius is R and it rolls with a linear speed v, what is the angular speed of the disk?
Correct Answer: Ο‰ = v/R
  • Step 1: Understand that the disk is rolling without slipping, which means there is a direct relationship between its linear speed and angular speed.
  • Step 2: Identify the variables: the linear speed of the disk is 'v' and the radius of the disk is 'R'.
  • Step 3: Recall the formula that relates linear speed (v) and angular speed (Ο‰) for rolling without slipping: Ο‰ = v / R.
  • Step 4: To find the angular speed (Ο‰), simply divide the linear speed (v) by the radius (R).
  • Rolling Motion – The relationship between linear speed and angular speed for an object rolling without slipping.
  • Angular Speed – The rate of rotation of an object, typically measured in radians per second.
  • Linear Speed – The speed at which the center of mass of the rolling object moves along a path.
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