CIE A Level Physics

Topic Questions

A LevelPhysicsCIETopic Questions12. Motion in a Circle12.2 Centripetal Acceleration

Syllabus Edition

First teaching 2020

Last exams 2024

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12.2 Centripetal Acceleration

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1a
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A centripetal force causes a centripetal acceleration. 

State two properties of the centripetal force that is required for this.

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1b
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State the equation for centripetal acceleration.               

[1]

State the definition and unit of each variable in part (i)              

    [3]

                                                    

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1c
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Calculate the angular speed of a satellite in a geostationary orbit. 

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1d
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The satellite has an altitude of 36 000 km. 

Calculate the centripetal acceleration of the satellite. 

Radius of Earth = 6400 km

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2a
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State what is meant by centripetal force.

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2b
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State the centripetal force in each of the following situations 

(i)
Venus orbiting the Sun
[1]
(ii)
a car driving around a roundabout
[1]
(iii)
rotating a ball tied to the end of a piece of string.
[1]

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2c
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The Moon orbits the Earth in a circular path. 

Explain, with reference to Fig 1.1, why the path of the moon is circular.

12-2-2c-e-field-lines-on-earth

 Fig 1.1

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2d
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The centripetal force of the Moon is 2.21 × 1020 N.  

Calculate the distance of the Moon from the surface of the Earth. 

Mass of the Moon = 7.35 × 1022 kg

Radius of Earth = 6.4 × 106 m

Linear speed of the Moon = 1023 m s–1

 

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3a
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Two of Jupiter's moons, Ganymede and Callisto orbit around Jupiter in a circular path, as shown in Fig 1.1. 

Fig 1.1 shows the North pole of Jupiter, where both moons orbit counter-clockwise.

12-2-3a-e-jupiter-moons
Fig 1.1
 

Identify, by drawing arrows, the following:

 
(i)
the centripetal force on each moon. Label this F.
[2]
 
(ii)
the linear velocity of each moon. Label this v.
[2]

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3b
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Both of Jupiter's moons travel at a speed of roughly 10 000 m s–1. 

State which moon will have a longer time period. Explain your answer.

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3c
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The centripetal acceleration of Ganymede is 0.11 m s–2.

The mass of Ganymede is 1.48 x 1023 kg. 

Determine the centripetal force on Ganymede.

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3d
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Explain how the centripetal force of an object with the same mass and orbit as Ganymede would compare if it travelled with twice the angular speed.

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1a
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Two runners are running around a circular track. One runner follows path X and the other follows path Y, as shown in Fig. 1.1.

 
12-2-1a-m-circular-running-track
Fig 1.1
 

The radius of path X is 36.50 m. Path Y is parallel to, and 1.2 m outside, path X. Both runners have mass 75 kg. The maximum lateral (sideways) friction force F that the runners can experience without sliding is 57 mN. 

Show that the maximum speed at which the runner on path Y can move is 0.17 m s–1.

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1b
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Compare the centripetal acceleration and maximum speed of the runner on path X compared to path Y.

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1c
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Calculate the time taken for the runner in path X to complete 1 lap.

 
T = ............................. minutes 

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1d
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The runner on path Y has an ankle injury that has come back with a vengeance, so it takes them twice as long to complete 1 lap.

Determine their new centripetal acceleration. 

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2a
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A bowl-shaped skating ramp can be modelled as a hollow sphere.

A skateboarder with a horizontal speed follows a circular path inside the bowl of radius 2.3 m, as shown in Fig 1.1.

12-2-2a-m-skateboarder-circular-motion

Fig 1.1

The forces acting on the skateboarder are their weight W and the normal reaction force R of the ramp on the skateboarder. R is at an angle θ to the horizontal. 

Sketch W, R and θ on Fig 1.2.
v09BaY6S_12-2-2a-m--forces-on-skateboarder
Fig 1.2

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2b
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Determine an equation for W in terms of θ and the resultant force, F on the skateboarder.

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2c
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Explain why force F is significant to the motion of the skateboarder.

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2d
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For the radius of the ramp in Fig 1.1, the skateboarder travels at a speed of 6.0 m s–1. 

Show that the angle θ is 32°.                          

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