Rotational Kinematics and the Angular Velocity Vector · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.
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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 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 divided by the time t
    • Omega equals omega zero plus alpha t
    • Angle equals omega squared over two

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

    • Two tangential accelerations acting together
    • Two centripetal accelerations acting together
    • Tangential from alpha plus centripetal inward

  5. A point sits 2 m from the fixed axis of a rigid body spinning with omega 3 radians per second. What is its linear speed, in metres per second?

    Answer: ______________

  6. A wheel starts from rest with constant angular acceleration 4 radians per second squared and spins for 5 seconds. What is its final omega, in radians per second?

    Answer: ______________

  7. A point sits 2 m from the fixed axis of a rigid body spinning with omega 4 radians per second. What is its centripetal acceleration, in metres per second squared?

    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 for all points
    • Equal omega with different radii gives different speeds
    • Hub points move faster than rim points on one wheel
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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 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 inward · 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 · Shared spin rate still scales into different speeds through radius.
Worksheet · LightMySky