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Physics · Grades 10–12

Circular motion: changing velocity at constant speed

Keep centripetal acceleration and actual force sources distinct.

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Learn the idea

Velocity

Velocity includes direction. Moving around a circle changes velocity even if speed is constant.

Acceleration

For uniform circular motion, acceleration magnitude is v squared over radius and points inward.

Force source

Centripetal names the required inward resultant, not a new force to add beside gravity, friction or tension.

Limits

The uniform circular model assumes constant speed and fixed radius. A changing speed can add a tangential acceleration.

Worked examples

An object travels at 6 m/s in a circle of radius 3 m. Find centripetal acceleration magnitude.

v²/r = 36/3 = 12 m/s².

12 m/s²

Why can constant speed around a circle involve acceleration?

Acceleration measures vector velocity change, not only change in speed.

Velocity direction changes.

Check your understanding

  1. A 2 kg mass needs centripetal acceleration 5 m/s². Find inward net force magnitude.

  2. Why is adding an extra centripetal force beside all the actual inward forces often double-counting?

  3. In uniform circular motion, acceleration points where?

    1. Always upward on the page
    2. Toward the centre
    3. Along the instantaneous tangent

Answers and marking notes

Answers and marking notes
  1. 10 N

    Fnet = ma = 2 × 5 = 10 N.

  2. Centripetal force is the name for their inward resultant, not an additional interaction.

    Credit identifying actual force sources.

  3. Toward the centre

    The direction changes inward as the object moves around the circle.

Further reading and review references

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Independent educational review required. Grade bands are approximate; these are not officially aligned curricula.