Rotational Dynamics and Rolling Without Slipping · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Rolling without slipping, and why shape wins races

Science · Forces & Motion · ages 20-22
Name ______________________   Date ____________

  1. A hoop and a solid cylinder start together at the top of a slope. Which reaches the bottom first?

    • The solid cylinder
    • The hoop
    • Both at the same time

  2. A wheel of radius R rolls without slipping. How is the centre speed v linked to the spin rate omega?

    • v equals omega divided by R
    • v equals R times omega
    • v equals R divided by omega

  3. Static friction between a rolling wheel and the ground does no work.

    Circle one:   True   False

  4. For a body rolling down a slope, which equation links the friction force to the change in spin?

    • Friction equals mass times centre acceleration
    • Friction times radius equals I times alpha
    • Friction times mass equals I times alpha

  5. A solid cylinder rolls down a slope of angle theta without slipping. What is its centre acceleration?

    • g sin theta
    • half g sin theta
    • two thirds g sin theta

  6. A driver floors the pedal and the tires spin while the car stays still. What happened to the rolling link?

    • The contact point slides, so centre speed no longer equals R omega
    • The grip holds, so centre speed still equals R omega
    • The spin stops mattering, so centre speed equals omega alone

  7. Lee says static friction slows the rolling cylinder and wastes its energy as heat. What is the error?

    • Static friction enables the roll and does no work, since its contact point rests
    • Static friction resists the roll and burns energy as heat
    • Static friction only appears after slipping starts

  8. Sam says the hoop wins the slope race because it is lighter. What is the mistake?

    • Mass decides the race, so the lighter hoop wins
    • The slope angle decides it, so both tie
    • Shape decides it: the hoop stores more energy in spin, so it loses
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Answer key

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Rolling without slipping, and why shape wins races W1-mt_1mV6ukwDxK-s1

  1. The solid cylinder · The hoop stores more energy in spin, so less remains for forward motion.
  2. v equals R times omega · Rolling without slipping locks forward motion to spin: v equals R omega.
  3. True · The contact point is at rest, so the force acts through no distance.
  4. Friction times radius equals I times alpha · Friction supplies the torque, and torque equals I times alpha.
  5. two thirds g sin theta · With I equal to half m R squared, the rolling formula gives two thirds g sin theta.
  6. The contact point slides, so centre speed no longer equals R omega · Spinning in place is slipping, so the contact slides and the link breaks.
  7. Static friction enables the roll and does no work, since its contact point rests · Static friction supplies the spin torque at a resting contact, so it costs no energy.
  8. Shape decides it: the hoop stores more energy in spin, so it loses · Mass cancels out of the race. Shape sets I, and the hoop wastes more on spin.
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