Centripetal acceleration

a = v²/r toward the centre — the acceleration that bends motion into a circle.

Centripetal acceleration0 min · Free lecture

In this lesson

  • a = v²/r toward the centre — the acceleration that bends motion into a circle.

The centre is the only direction that bends — every other component would change the speed.

a_c = v²/r = ω²r = 4π²r/T². It exists whenever motion is curved — even at constant speed.

Common error: mixing v = rω with a = v²/r without converting units (rpm → rad/s).

ac=v2r=ω2r=4π2rT2a_c = \frac{v^2}{r} = \omega^2 r = \frac{4\pi^2 r}{T^2}

Centripetal acceleration forms

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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Centripetal acceleration — FemtoLearn.
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a = v²/r toward the centre — the acceleration that bends motion into a circle.
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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 · Numerical · difficulty 1/5

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

  3. Q3 · 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.

  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