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What is the condition for rolling without slipping?

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Question: What is the condition for rolling without slipping?

Options:

  1. v = Rω
  2. v = 2Rω
  3. v = 0
  4. v = R^2ω

Correct Answer: v = Rω

Solution: 

The condition for rolling without slipping is that the linear velocity v of the center of mass is equal to the product of the radius R and the angular velocity ω, i.e., v = Rω.

What is the condition for rolling without slipping?

Practice Questions

Q1
What is the condition for rolling without slipping?
  1. v = Rω
  2. v = 2Rω
  3. v = 0
  4. v = R^2ω

Questions & Step-by-Step Solutions

What is the condition for rolling without slipping?
Correct Answer: v = Rω
  • Step 1: Understand that 'rolling without slipping' means that the object rolls on a surface without sliding.
  • Step 2: Identify the center of mass of the rolling object, which is the point where its mass is evenly distributed.
  • Step 3: Know that 'linear velocity' (v) is how fast the center of mass is moving in a straight line.
  • Step 4: Recognize that 'angular velocity' (ω) is how fast the object is rotating around its center.
  • Step 5: Remember that the radius (R) is the distance from the center of the object to its edge.
  • Step 6: The condition for rolling without slipping is that the linear velocity (v) of the center of mass equals the radius (R) multiplied by the angular velocity (ω).
  • Step 7: Write the equation: v = Rω.
  • Rolling Motion – The relationship between linear and angular motion in rolling objects.
  • Velocity and Angular Velocity – Understanding how linear velocity relates to angular velocity through the radius.
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