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If a rolling object has a translational speed of v and a rotational speed of ω,

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Question: If a rolling object has a translational speed of v and a rotational speed of ω, what is the relationship between them for rolling without slipping?

Options:

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

Correct Answer: v = ωR

Solution: 

For rolling without slipping, the relationship is v = ωR, where v is the translational speed and ω is the angular speed.

If a rolling object has a translational speed of v and a rotational speed of ω,

Practice Questions

Q1
If a rolling object has a translational speed of v and a rotational speed of ω, what is the relationship between them for rolling without slipping?
  1. v = ωR
  2. v = 2ωR
  3. v = ω/R
  4. v = R/ω

Questions & Step-by-Step Solutions

If a rolling object has a translational speed of v and a rotational speed of ω, what is the relationship between them for rolling without slipping?
Correct Answer: v = ωR
  • Step 1: Understand that 'rolling without slipping' means the object rolls on a surface without sliding.
  • Step 2: Identify the terms: 'v' is the translational speed (how fast the center of the object moves), and 'ω' is the rotational speed (how fast the object spins around its axis).
  • Step 3: Recognize that when an object rolls without slipping, the point of contact with the ground is momentarily at rest.
  • Step 4: Relate the translational speed 'v' to the rotational speed 'ω' using the radius 'R' of the object.
  • Step 5: The formula that connects these speeds is v = ωR, meaning the translational speed equals the rotational speed multiplied by the radius.
  • Rolling Motion – The relationship between translational speed and rotational speed for an object rolling without slipping.
  • Kinematics – Understanding the connection between linear and angular motion.
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