Uniform circular motion

Constant speed, but accelerating: the velocity turns, so a = v²/r toward the centre.

Uniform circular motion0 min · Free lecture

In this lesson

  • Constant speed, but accelerating: the velocity turns, so a = v²/r toward the centre.

The hardest idea in rotation: uniform speed still means acceleration.

In UCM, |v| is constant but the direction changes at rate ω. The acceleration is purely centripetal: a_c = v²/r = ω²r, pointing to the centre.

The change in velocity over a quarter turn is v√2 — not zero — the classic proof that acceleration exists.

ac=v2r=ω2ra_c = \frac{v^2}{r} = \omega^2 r

Centripetal acceleration

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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Uniform circular motion — FemtoLearn.
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Constant speed, but accelerating: the velocity turns, so a = v²/r toward the centre.

Frequently asked

Is there acceleration if speed is constant?

Yes — direction changes, so velocity changes.

Printable notes (free)

Practice

Free · 4 questions with full solutions
  1. Q1 · 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.

  2. Q2 · 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
  3. Q3 · Numerical · difficulty 1/5

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

  4. Q4 · 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.