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Centripetal acceleration and force

G2.8 G2.9 G5.1

By the end of this lesson you should be able to

  • Describe the concepts of centripetal acceleration and centripetal force. G2.8
  • Solve problems involving forces acting on objects in uniform circular motion using F_c = F_net = mv^2/r. G2.9
  • Consider how an object can travel at a constant speed yet be accelerating. G5.1

Key ideas

  • Because the velocity's direction changes, there is an acceleration: the centripetal acceleration, pointing to the centre.
  • A net inward force (the centripetal force) is needed. It is not a new force: it is provided by a real force such as tension, friction, gravity or the normal force.
  • There is no outward 'centrifugal' force in an inertial frame. The outward feeling is your inertia.
  • The force is perpendicular to the velocity, so it changes direction but not speed.

Key formulas (QCAA formula book notation)

\[ a_c = \frac{v^2}{r} \]
\[ F_c = F_{net} = \frac{m v^2}{r} \]
Worked example

A 0.20 kg ball on a 0.80 m string is whirled horizontally at 5.0 m s⁻¹. Find the tension (ignore gravity's effect on the string angle).

  1. \(F_c = 0.20 \times 5.0^2 / 0.80 = 6.3\) N, provided by the tension

Common mistakes

  • Drawing a centripetal force as well as the real force on a free-body diagram.
  • Forgetting to square v.
  • Pointing the acceleration along the velocity.

Do

  • Read: Textbook (Oxford Physics for Queensland Units 3 & 4) section 4.3
  • Do: CYL 4.3 Q3, 4, 6, 9

Try it

Watch

Further reading

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