Angular acceleration

α = dω/dt — the rate of change of angular velocity.

Angular acceleration0 min · Free lecture

In this lesson

  • α = dω/dt — the rate of change of angular velocity.

A fan speeding up or slowing down has angular acceleration either way.

α = dω/dt = d²θ/dt². Constant α gives the rotational SUVAT twins: ω = ω₀ + αt, θ = ω₀t + ½αt², ω² = ω₀² + 2αθ.

Every 1D linear formula maps to rotation by replacing x→θ, v→ω, a→α — the analogies are exact for constant α.

ω=ω0+αt,θ=ω0t+12αt2\omega = \omega_0 + \alpha t,\quad \theta = \omega_0 t + \tfrac{1}{2}\alpha t^2

Rotational equations of motion

Worked example

In uniform circular motion, the acceleration of the particle is directed:

  1. Speed is constant but velocity direction changes continuously.
  2. The change in velocity points toward the centre → centripetal acceleration a_c = v²/r toward the centre.

Answer: Toward the centre of the circle

Transcript (0 min)
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Angular acceleration — FemtoLearn.
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α = dω/dt — the rate of change of angular velocity.
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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 particle moves on a circle of radius 1.5 m with constant speed 6 m/s. Find the magnitude of its centripetal acceleration.

  4. Q4 · MCQ · difficulty 1/5

    In uniform circular motion, the acceleration of the particle is directed:

    • Along the tangent to the circle
    • Toward the centre of the circle
    • Away from the centre of the circle
    • It is zero