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Circular Motion

Vertical circular motion

  • 3 things to know
  • A2 Unit 3

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Recall questions on Vertical circular motion.

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Key term

Write the equation relating the forces on a ball at the top of a vertical circle to its centripetal acceleration.

Key term

Which forces provide the centripetal force on a ball at the top of a vertical circle on the end of a string?

Key term

Write the equation relating the forces on a ball at the lowest point of a vertical circle to its centripetal acceleration.

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    Which forces provide the centripetal force on a ball at the top of a vertical circle on the end of a string?

    Model answer

    The tension in the string and the weight of the ball both act downwards towards the centre of the circle, and together they provide the centripetal force.

  2. 2

    Write the equation relating the forces on a ball at the top of a vertical circle to its centripetal acceleration.

    Model answer

    T + mg = mv²/r, where T is the tension in newtons, m the mass in kilograms, v the speed in m s⁻¹ and r the radius in metres.

  3. 3

    Write the equation relating the forces on a ball at the lowest point of a vertical circle to its centripetal acceleration.

    Model answer

    T − mg = mv²/r, because the weight now acts away from the centre while the tension acts towards it.

  4. 4

    At which point of a vertical circle is the tension in the string greatest, and why?

    Model answer

    It is greatest at the lowest point, because there the tension must both support the weight of the ball and supply the whole of the centripetal force.

  5. 5

    Derive an expression for the minimum speed at the top of a vertical circle if the string is to stay taut.

    Model answer

    The limiting case is zero tension, so the weight alone provides the centripetal force and mg = mv²/r. The minimum speed is therefore v = √(gr).

  6. 6

    Calculate the minimum speed at the top of a vertical circle of radius 0.80 m for a ball on a string to keep the string taut, taking g as 9.81 m s⁻².

    Model answer

    The minimum speed is √(9.81 × 0.80) = 2.80 m s⁻¹.

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