Angular quantities: the complete set

θ, ω, α with their linear partners s, v, a_t — one table, exact analogies.

Angular quantities: the complete set0 min · Free lecture

In this lesson

  • θ, ω, α with their linear partners s, v, a_t — one table, exact analogies.

Translation and rotation are the same physics in two languages.

The mapping: x↔θ, v↔ω, a↔α, m↔I, F↔τ, p↔L. All kinematic equations carry over verbatim for constant α.

Learn the analogy table once and both chapters (kinematics + rotation) get easier together.

s=rθ, v=rω, at=rαs = r\theta,\ v = r\omega,\ a_t = r\alpha

The linear-angular bridge

Worked example

A disc's angular position is θ = 2t² rad. Find its angular velocity at t = 3 s.

  1. ω = dθ/dt = 4t.
  2. At t = 3: ω = 12 rad/s.

Answer: 12

Transcript (0 min)
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Angular quantities: the complete set — FemtoLearn.
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θ, ω, α with their linear partners s, v, a_t — one table, exact analogies.
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Practice

Free · 4 questions with full solutions
  1. Q1 · Numerical · difficulty 1/5

    A wheel rotates at 270 rpm. What is its angular velocity in rad/s?

  2. Q2 · Numerical · difficulty 1/5

    A point is at distance 1.7 m from the axis of a wheel rotating with angular velocity 11 rad/s. Find its linear speed.

  3. Q3 · Numerical · difficulty 2/5

    A disc's angular position is θ = 2t² rad. Find its angular velocity at t = 3 s.

  4. Q4 · Numerical · difficulty 2/5

    A particle moves on a circle of radius 1.5 m with constant speed 6 m/s. Find the magnitude of its centripetal acceleration.