Angular velocity

ω = dθ/dt — how fast the angle changes; positive counterclockwise.

Angular velocity0 min · Free lecture

In this lesson

  • ω = dθ/dt — how fast the angle changes; positive counterclockwise.

A ceiling fan's 'speed' is angular velocity — every blade shares it.

ω = dθ/dt (average: Δθ/Δt). For a rigid body, ω is the same for every point — the fundamental advantage of angular variables.

Direction along the rotation axis (right-hand rule). Rad/s is the SI unit.

ω=dθdt\omega = \frac{d\theta}{dt}

Angular velocity

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 velocity — FemtoLearn.
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ω = dθ/dt — how fast the angle changes; positive counterclockwise.
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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.