Rotational Kinematics and the Angular Velocity Vector · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

How spin is measured

Science · Forces & Motion · ages 20-21
Name ______________________   Date ____________

  1. Rotation maths needs angles in radians, since arc length equals radius times angle only in radians.

    Circle one:   True   False

  2. A wheel spins one way, then reverses. What happens to the angular velocity vector?

    • It flips to point the opposite way
    • It stays pointing the same way
    • It shrinks to zero forever

  3. A wheel spins up steadily from rest with constant angular acceleration. Which equation gives omega after time t?

    • Omega equals alpha over t
    • Omega equals omega zero plus alpha t
    • Angle equals omega squared

  4. A point rides a wheel that is spinning up. Which pair of accelerations acts on it?

    • Two tangential accelerations
    • Two centripetal accelerations
    • Tangential from alpha plus centripetal toward the centre

  5. A point sits at radius 2 on a body spinning with omega 3. What is its linear speed?

    Answer: ______________

  6. A wheel starts from rest with angular acceleration 4 and spins for 5 seconds. What is its final omega?

    Answer: ______________

  7. A point at radius 2 spins with omega 4. What is its centripetal acceleration?

    Answer: ______________

  8. A student claims the rim and the hub of one rigid wheel share the same linear speed because they share one omega. What is wrong?

    • Nothing, equal omega means equal speed
    • Equal omega with different radii gives different speeds, since v equals r omega
    • Hub points move faster than rim points
LightMySky · lightmysky.comW1-mt_2UqK-zViqf-s1

Answer key

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

How spin is measured W1-mt_2UqK-zViqf-s1

  1. True · The radius bridge between spin and travel assumes radian measure.
  2. It flips to point the opposite way · Reversing the spin reverses the curled fingers, so the thumb flips.
  3. Omega equals omega zero plus alpha t · Constant alpha mirrors constant linear acceleration term by term.
  4. Tangential from alpha plus centripetal toward the centre · Changing spin rate gives the tangential part; turning gives the inward part.
  5. 6 · Linear speed is radius times angular speed.
  6. 20 · Omega equals omega zero plus alpha t with omega zero 0.
  7. 32 · Centripetal size is radius times omega squared, always inward.
  8. Equal omega with different radii gives different speeds, since v equals r omega · Shared spin rate still scales into different speeds through radius.
Worksheet · LightMySky