AQA A Level Physics

Topic Questions

6.1 Circular Motion

1a6 marks

Table 1

Physical Quantity

Scalar or Vector

Velocity

 

Centripetal Acceleration

 

Speed

 

Distance Travelled

 

Centripetal Force

 

Angle

 

 

Complete the right-hand column of Table 1 stating whether each physical quantity is a scalar or vector.

1b3 marks

The centripetal force, F is defined by the equation: 

         F = mω2r 

State the definition of the following variables and an appropriate unit for each.        

             (i)         m 

            (ii)         ω 

            (iii)          r

1c2 marks

A car travels around a roundabout, as shown in Figure 1. 

Figure 1

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(i)
Draw an arrow on Figure 1 to show the direction of the centripetal force on the car.   
(ii)
State the name of the force that supplies this centripetal force.      
1d3 marks

The mass of the car is 1600 kg. It turns with an angular speed of 0.6 rad s–1 which causes the driver to experience a centripetal force of 8600 N. 

Calculate the radius of the roundabout.

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2a1 mark

Melody is playing a game of swing ball. The game consists of a ball attached by a short rope to the top of a pole to rotate around it. The ball is kept it motion in a circular path after being hit by a bat, as shown in Figure 1. 

Figure 1

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State the equation linking the angular velocity of the ball ω, rotation angle, θ and time, t.

2b2 marks

The ball rotates by 30º in 0.7 s. 

Convert 30º into radians. State your answer in terms of π.

2c3 marks

Hence, or otherwise, calculate ω and state an appropriate unit.

2d3 marks

The rope is 80 cm long.

Calculate the initial velocity of the ball if it was to suddenly separate from the rope.

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3a3 marks

A centrifuge is often used in astronaut training. This is to simulate Earth’s gravity on board the space station. A simplified diagram is shown in Figure 1 where the astronauts sit in a cockpit at the end of each arm, each rotating about an axis at the centre. 

Figure 1

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At its top speed, the centrifuge makes 1 full rotation every 1.30 s. 

Calculate the frequency of the centrifuge. State an appropriate unit and express your answer to an appropriate number of significant figures.

3b2 marks

Calculate the angular speed of the centrifuge in rad s–1.

3c2 marks

Each astronaut is placed 6.20 m from the rotation axis. 

Calculate the magnitude of the centripetal acceleration on each astronaut.

3d1 mark

Sketch the direction of the acceleration on each astronaut in Figure 1.

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4a2 marks

Explain what is meant by the centripetal force.

4b2 marks

Explain what is meant by centripetal acceleration.

4c2 marks

The centripetal acceleration, a is defined as 

         a = begin mathsize 16px style v squared over r end style

where v is the linear velocity of an object and r is the radius of its orbit. 

The centripetal force, F is defined as 

         F = fraction numerator m v squared over denominator r end fraction

where m is the mass of the object. 

Explain how the centripetal force, F equation is derived from the equation for a.

4d5 marks

Complete the sentences by using an answer from the box. 

You may use a word once, more than once or not at all. 

Speed

Scalar

Velocity

Direction

Vector

Centripetal

Magnitude

Accelerating

 

An object travelling in a circular path is _________, even though it is moving at constant _________. 

Speed is a _________quantity, which means it only has _________. 

Velocity, however, is a _________quantity which means it has both _________and _________. 

Since the object is constantly changing _________, this means it is constantly changing _________, but not its _________. 

The acceleration is the rate of change of velocity, therefore the object must be _________.

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5a3 marks

The London Eye shown in Figure 1 has a radius of approximately 68 m and the passengers in the capsules travel at an angular speed of 3.5 × 10–3 rad s–1. 

Figure 1

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Calculate the speed of each passenger in the capsules.

5b2 marks

Sketch on any capsule in Figure 1: 

(i)         The direction of the centripetal force. Label this F. 

(ii)        The direction of the linear speed. Label this v. 

Assume the London Eye is rotating clockwise.

 

5c3 marks

Each capsule weighs about 98.1kN. 

Calculate the centripetal force on an empty capsule.

5d5 marks

Dan has travelled to London to watch an exciting Physics show. Being an eager tourist, he arrives early and plans to ride the London Eye. When he gets to the front of the queue however, he realises he only had 40 minutes before he needs to leave for the show. 

State, with a calculation, whether Dan is still able to ride the London Eye and leave to see the show on time.

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1a4 marks

A ‘loop the loop’ is a vertical circular path. Figure 1 shows a toy car of mass 80 g completing a ‘loop the loop’ which has a radius of 0.15 m. 

Figure 1

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The car enters the loop with a speed of 2.0 m s–1 and then undergoes a constant deceleration until it passes A with a speed of 1.0 m s–1

After A, the car undergoes a constant acceleration before leaving the loop with a speed of 2.0 m s–1 

(i)
Calculate the time taken for a car to complete the ‘loop the loop’.         
(ii)
Sketch a velocity-time graph for the journey through the loop. Mark the time at which the car passes position A.  
1b4 marks
(i)
Describe the origin of the centripetal force that keeps the car on the track throughout the loop.
(ii)
Calculate the minimum and maximum values of the centripetal force experienced by the car.  
1c3 marks

For the journey through the loop, sketch a graph to show how the vertical component of the force on the car varies with the angle rotated by the car around the loop. 

Include the values for the maximum and minimum forces on the car. 

Only show the general shape between these values.

1d4 marks

A student is investigating the energy changes in a ‘loop the loop’, as shown in Figure 2.

They want to determine the minimum height, h, required for a toy car of mass m to complete a loop the loop or radius r, when starting from rest. 

Figure 2

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Show that the minimum height, h is:

                  h equals 5 over 2 r

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2a2 marks

A proton of mass m subscript P is moving in a circle at constant speed. The time period of the particle’s rotation is T and its kinetic energy is E.

Show that the radius of the particle’s path is given by the formula: 

         r =square root of fraction numerator E T squared over denominator 2 pi squared m subscript p end fraction end root

2b3 marks

Figure 1 shows the path of the proton moving anti-clockwise in a circle at constant speed. The proton travels 1.24 mm during one full revolution. 

Figure 1

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The net force acting on the proton is 64 fN.  

Show that the speed of the proton is 8.7 × 104 ms–1.

2c3 marks

Calculate the frequency of rotation of the proton.

2d2 marks

Explain why the work done by the centripetal force on the proton is zero.

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3a3 marks

A small ball is attached to a string and moves in a circle with constant angular speed, omega. The angle between the string and the vertical is θ, as shown in Figure 1 

Figure 1

6-1-s-q--q3a-hard-aqa-a-level-physics

Show that the radius of the ball’s path can be given by the formula: 

         r  = fraction numerator g space tan space theta over denominator omega squared end fraction

3b4 marks

The ball has a mass of 413 g and the angle between the string and the vertical θ is 19°. It rotates with an angular speed of 3.42 rad s-1. 

Calculate the radius of the ball’s path. 

Give your answer to an appropriate number of significant figures.

3c2 marks

Determine the number of oscillations per minute that the ball completes, assuming its angular speed remains constant.

3d2 marks

Explain the effect upon the oscillations per minute of extending the length of the string, whilst keeping the radius of the circular motion, r, constant. 

Assume the mass of the string is negligible.

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4a4 marks

A satellite orbits the Earth, as shown in Figure 1. It remains in orbit due to the gravitational field of the Earth.

Figure 1

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It takes the satellite 100 minutes to complete one full revolution around the Earth. The mass of the Earth is 6.0×1024 kg and the radius of the Earth is 6400 km. 

Show that the distance of the space telescope from the surface of the Earth is approximately 750 km.

4b4 marks

A manned space station orbits at a distance of 1500 km from the surface of the Earth. 

Calculate the orbital period of the space station.

4c2 marks

During an emergency, the space station in part (b) needs to rendezvous with the satellite in part (a). 

Determine the increase in the orbital speed of the space station as moves from orbiting at its original height to the height of the satellite

4d2 marks

The space station is required to tether itself to the satellite. This requires the two to be joined by a 20 m cord, as shown in Figure 2. 

Figure 2

6-1-s-q--q4d-hard-aqa-a-level-physics

Explain why the arrangement shown in Figure 2 will require the space station to use some of its fuel whilst tethered at this height if it wishes to maintain the original orbital period of the satellite. 

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5a2 marks

A roller coaster cart is travelling over a section of track, shown in Figure 1, at a constant speed, v. N passengers have an average mass, m subscript P , and the cart has a mass, m subscript C. An electric motor on the cart is used so it can maintain its speed as it climbs, and then goes over a bump in the track, that has a radius of the curvature equal to r. 

Figure 1

6-1-s-q--q5a-hard-aqa-a-level-physics

Determine a general formula for the amount of electrical energy, E subscript E, that needs to be used to maintain the speed v, over the bump.

5b2 marks

The radius of the curvature of the path of the passengers is 21 m, and the cart maintains a speed of 8 m s-1. The average mass of the passenger, m subscript P,  is 56 kg.

If 5 passengers ride the cart over the bump together, estimate the change in the contact force, R, between the passenger and the seat of the cart as the car travels over the highest point of the bump.

5c6 marks

A banked turn is a section of road that is angled so that cars can travel around corners at a higher velocity without the aid of friction

Several racetracks have banked turns that are curved, such that the angle of the track increases as the distance from the inside edge of the track increases. An image of such a track is shown in Figure 2

Figure 2

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Discuss the motion of the car as it travels around the banked turn. In your answer you should: 

  • Explain how Newton’s three laws of motion apply to its motion in a circle
  • Explain the effect of changing the angle of the road, and the speed of the car, on its motion 

You may wish to draw a diagram to clarify your answer.

The quality of your written communication will be assessed in your answer.

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1a3 marks

A lead ball of mass 0.45 kg is swung round on the end of a string so that the ball moves in a horizontal circle of radius 1.3 m. The ball travels at a constant speed of 7.2 m s–1. 

Calculate the time taken for the string to turn through an angle of 190º.

1b2 marks

Calculate the tension in the string.           

You may assume that the string is horizontal.

1c2 marks

The string will break when the tension exceeds a maximum tension. The ball makes two revolutions per second at the maximum tension of the string. 

Calculate the tension above which the string will break.

1d6 marks

Discuss the motion of the ball in terms of the forces that act on it. In your answer you should: 

  • Explain how Newton’s three laws of motion apply to its motion in a circle
  • Explain why, in practice, the string will not be horizontal. 

You may wish to draw a diagram to clarify your answer.

The quality of your written communication will be assessed in your answer.

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2a2 marks

Explain why a particle moving in a circle with uniform speed is accelerating.

2b2 marks

Figure 1 shows a fairground ride called a Rotor. Riders stand on a wooden floor and lean against the cylindrical wall. 

Figure 1

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The fairground ride is then rotated. When the ride is rotating sufficiently quickly the wooden floor is lowered. The riders remain pinned to the wall by the effects of the motion. When the speed of rotation is reduced, the riders slide down the wall and land on the floor. 

At the instant shown in Figure 2 the ride is rotating quickly enough to hold a rider at a constant height when the floor has been lowered. 

Figure 2

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Explain why the riders slide down the wall as the ride slows down.

2c2 marks

A rotor accelerates uniformly from rest to maximum angular velocity of 3.6 rads s–1. 

At the maximum speed the centripetal acceleration is 35 m s–2. 

Calculate the diameter of the rotor.

2d4 marks

Figure 3 shows the final section of a roller coaster which ends in a vertical loop. Cars on the roller coaster descend to the start of the loop and then travel around it. 

Figure 3

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As the passengers move around the circle from A to B to C, the reaction force between exerted by their seat varies. 

State the position at which this force will be a maximum and the position at which it will be a minimum. Explain your answers.        

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3a3 marks

Figure 1 below shows a child at position B on a rotating playground roundabout. Frictional forces act on the child to keep them in the same position. 

Figure 1

6-1-s-q--q3a-medium-aqa-a-level-physics

The child is at a distance of 0.153 m from the centre of the centre of the roundabout. The linear speed of the child at B is 1.12 m s–1. 

Calculate the revolutions per minute of the roundabout.

3b1 mark

Mark on Figure 1 an arrow to show the direction of the resultant horizontal force on the child.

3c3 marks

The child has a mass of 20 kg. 

Calculate the centripetal acceleration and centripetal force at position B.

3d4 marks

The roundabout has an inner railing to hold onto at its centre. There is another railing near the outer edge. 

Whilst the roundabout is rotating, state which railing would be easier to hold onto for the child and suggest why this would be so.

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4a3 marks

Figure 1 shows a ball of mass 160 g, which is fixed to the end of a light string of length 35 cm, is released from rest at X. It swings in a circular path, passing through the lowest point Y at speed v. 

Figure 1

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Calculate the velocity of the mass at Y

4b2 marks

Calculate the centripetal force acting on the mass.

4c2 marks

Calculate the tension in the string.

4d3 marks

The ball is replaced with a smaller ball of mass m attached to the same string and travels at a speed of 3.5 m s–1 at point Y. The ball swings in a circular path identical to the one in Figure 1. 

If the tension of the string remains the same at point Y, calculate the mass m.

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5a2 marks

Figure 1 shows a section of a roller coaster carrying a passenger over a curve in the track. The radius of curvature of the path of the passenger is r and the roller coaster is travelling at constant speed v. The mass of the passenger is m. 

Figure 1

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(i)
Draw and label arrows on Figure 2 to show the forces that act on the passenger as they pass over the highest point on the curved track.
(ii)
Write down an equation that relates the contact force R between the passenger and the seat to m, v, r and the gravitational field strength, g.   
                           
Figure 2

6-1-s-q--q5a-fig-2-medium-aqa-a-level-physics

5b3 marks

At a particular point on the track, the car moves with a linear velocity of 20 m s–1. The reaction force between the car and the track at this point is 200 N and the passenger has a mass of 70 kg. 

Calculate the distance from the passenger to the centre of curvature of the curved track.

5c2 marks

State and explain what would happen to the magnitude of R if the rollercoaster passed over the curved track at a higher speed.

5d3 marks

When the rollercoaster passes over a curved section of a track above a certain speed, the passenger is momentarily lifted off their seat and experiences weightlessness. 

Calculate the speed at which the rollercoaster must be travelling for the passenger to experience weightlessness.

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