Circular motionAQA A-Level Physics: Subtopic test

1. 1
   A stone of mass 0.15 kg is whirled in a horizontal circle of radius 0.80 m on a light string. It moves at a constant speed and completes 2.5 revolutions every second.

   (a)

   What is the angular speed of the stone?

   [1 mark]

   • A2.5 rad s⁻¹
   • B16 rad s⁻¹
   • C5.0 rad s⁻¹
   • D0.40 rad s⁻¹

   (b)

   What is the speed of the stone?

   [1 mark]

   • A2.0 m s⁻¹
   • B15.7 m s⁻¹
   • C12.6 m s⁻¹
   • D5.0 m s⁻¹

   (c)

   Explain why the stone is accelerating although its speed is constant.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A car of mass 1200 kg travels at a constant speed of 18 m s⁻¹ round a flat circular bend of radius 60 m. The only horizontal force on the car is the sideways friction between the tyres and the road.

   (a)

   What is the centripetal acceleration of the car?

   [1 mark]

   • A5.4 m s⁻²
   • B0.30 m s⁻²
   • C0.19 m s⁻²
   • D324 m s⁻²

   (b)

   What is the magnitude of the friction force on the car?

   [1 mark]

   • A3.6 × 10² N
   • B1.2 × 10⁴ N
   • C3.9 × 10⁵ N
   • D6.5 × 10³ N

   (c)

   The maximum friction force that the tyres can provide on a wet road is 8.0 kN. Calculate the maximum constant speed at which the car can take the bend.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A laboratory centrifuge spins sample tubes about a vertical axis at 6000 revolutions per minute. The base of each tube is 0.12 m from the axis of rotation.

   (a)

   Calculate the angular speed of the tubes and the speed of the base of a tube.

   [3 marks]

   (b)

   A sample of mass 5.0 g is at the base of a tube. Calculate the centripetal acceleration of the sample and the resultant force on it. Hence express the acceleration as a multiple of g, where g = 9.81 m s⁻².

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A fairground ride is a vertical cylindrical drum of radius 2.5 m that spins about its vertical axis. Riders stand against the inside wall and, once the drum is rotating at 0.55 revolutions per second, the floor is lowered. A rider of mass 60 kg stays pressed against the wall without sliding downwards. Take g = 9.81 m s⁻².

   (a)

   Explain how the rider is kept against the wall of the drum when the floor is lowered, and calculate the resultant force on the rider.

   [6 marks]

   (b)

   The operator proposes to increase the rate of rotation to 0.80 revolutions per second so that riders feel more secure. Evaluate this proposal by calculating the new centripetal acceleration as a multiple of g, comparing it with the original, and considering the friction needed to hold a rider.

   [6 marks]

   Total for question 4: 12 marks

End of questions