Non-uniform circular motion

Speed changes: tangential acceleration rα plus centripetal v²/r — both present, both needed.

Non-uniform circular motion0 min · Free lecture

In this lesson

  • Speed changes: tangential acceleration rα plus centripetal v²/r — both present, both needed.

A roller coaster speeds up at the bottom: centripetal still points up, tangential points forward.

Break the acceleration into radial (v²/r) and tangential (dv/dt) parts. The radial part always needs a force; the tangential part changes speed.

Problems give v(t) or ask for power: P = F_t·v with F_t = ma_t.

arad=v2r,atan=dvdta_{rad} = \frac{v^2}{r},\quad a_{tan} = \frac{dv}{dt}

The two components

Worked example

A particle moves on a circle of radius 2 m; its speed grows at 3 m/s² while its speed is 4 m/s. Find the magnitude of the total acceleration.

  1. Centripetal: a_c = v²/r = 16/2 = 8 m/s².
  2. Tangential: a_t = 3 m/s² (given).
  3. Total: a = √(8² + 3²) = √73 ≈ 8.54 m/s².

Answer: √73 ≈ 8.54 m/s².

Transcript (0 min)
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Non-uniform circular motion — FemtoLearn.
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Speed changes: tangential acceleration rα plus centripetal v²/r — both present, both needed.
Printable notes (free)

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