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When a wheel rolls without slipping, what is the relationship between the distan

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Question: When a wheel rolls without slipping, what is the relationship between the distance traveled by the center of mass and the angle rotated?

Options:

  1. d = Rθ
  2. d = 2Rθ
  3. d = R/2θ
  4. d = 3Rθ

Correct Answer: d = Rθ

Solution: 

The distance traveled by the center of mass d is equal to the product of the radius R and the angle rotated θ in radians, i.e., d = Rθ.

When a wheel rolls without slipping, what is the relationship between the distan

Practice Questions

Q1
When a wheel rolls without slipping, what is the relationship between the distance traveled by the center of mass and the angle rotated?
  1. d = Rθ
  2. d = 2Rθ
  3. d = R/2θ
  4. d = 3Rθ

Questions & Step-by-Step Solutions

When a wheel rolls without slipping, what is the relationship between the distance traveled by the center of mass and the angle rotated?
  • Step 1: Understand that when a wheel rolls without slipping, it moves forward while also rotating.
  • Step 2: Identify the radius (R) of the wheel, which is the distance from the center of the wheel to its edge.
  • Step 3: Recognize that the angle (θ) represents how much the wheel has rotated, measured in radians.
  • Step 4: Realize that for every complete rotation of the wheel, the distance it travels forward is equal to the circumference of the wheel, which is 2πR.
  • Step 5: Note that if the wheel rotates by an angle θ (in radians), the distance traveled by the center of mass (d) is directly proportional to both the radius and the angle rotated.
  • Step 6: Write the relationship as a formula: d = Rθ, where d is the distance traveled, R is the radius, and θ is the angle in radians.
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