Angular Momentum and Its Conservation · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.
به انگلیسی

Spin is conserved: skaters, tops, and gyroscopes

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

  1. A spinning skater pulls her arms tight to her body, with negligible external torque about her spin axis. What happens to her spin rate?

    • It slows down
    • It stays the same
    • It speeds up

  2. A rigid body with cylindrical symmetry spins about its principal axis with moment of inertia I and spin rate omega. What is its angular momentum?

    • m times v
    • I times omega
    • I divided by omega

  3. Pushing straight through the axle of a spinning wheel changes its spin.

    Circle one:   True   False

  4. A particle of mass 2 kg moves at 3 metres per second along a straight line. Its closest approach to a chosen point is 4 m. What is the size of its angular momentum about that point?

    • 24 kilogram metres squared per second
    • 12 kilogram metres squared per second
    • 6 kilogram metres squared per second

  5. A skater spins at 2 turns per second with arms out, then pulls in until her moment of inertia is halved, with negligible external torque. What is her new spin rate?

    • 4 turns per second
    • 2 turns per second
    • 1 turn per second

  6. A fast symmetric top, tilted and pivoted at its tip, leans while gravity pulls its centre down. Instead of falling, its axis slowly circles the vertical. Why?

    • The torque fades away as the top spins, leaving nothing to topple it
    • Gravity stops pulling on a spinning top, so no torque acts at all
    • The torque nudges the spin axis sideways, sweeping it around

  7. A diver tucks to spin faster, with negligible external torque about her spin axis. A student claims her angular momentum grew. How do you check the claim with the checklist?

    • Tucking adds outside torque, which raises her total angular momentum over time
    • Her spin inertia shrank, so her rate grew while total L stayed fixed
    • Air resistance acted as an outside torque and raised her L

  8. A student says a fast symmetric gyroscope, tilted and pivoted at its tip, stays upright because no torque acts on it. What is the error?

    • Gravity still torques it, but the torque turns the spin axis instead of toppling it
    • Gyroscopes feel no gravity at all, so no torque can ever act on them to tilt them over
    • The spin cancels gravity completely, so the top feels no downward pull at all
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Spin is conserved: skaters, tops, and gyroscopes W1-mt_9v3S9-rhwc-s1

  1. It speeds up · Her inertia shrinks, so her spin rate must grow to keep L fixed.
  2. I times omega · On a fixed axle, angular momentum is moment of inertia times spin rate.
  3. False · A push through the axle exerts no torque about it, so the spin is unchanged.
  4. 24 kilogram metres squared per second · Angular momentum is r cross p. The size is r times p times sine of the angle between them. At closest approach the velocity is perpendicular to r, so the size is 4 times 2 times 3, which is 24.
  5. 4 turns per second · Halving I doubles omega, since their product stays constant.
  6. The torque nudges the spin axis sideways, sweeping it around · The torque changes the direction of L, not its size, producing precession.
  7. Her spin inertia shrank, so her rate grew while total L stayed fixed · Name the torques first: none outside act, so L before equals L after.
  8. Gravity still torques it, but the torque turns the spin axis instead of toppling it · The torque is real. It redirects L sideways, which is precession.
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