Page 275 - Physics Coursebook 2015 (A level)

Chapter 17: Circular motion
something travel along a circular path. It does not tell us what causes this force, which might be gravitational, electrostatic, magnetic, frictional or whatever.
velocity
Earth
Figure 17.8 The gravitational pull of the Sun provides the centripetal force that keeps the Earth in its orbit.
QUESTIONS
10 In each of the following cases, state what provides the centripetal force:
a the Moon orbiting the Earth
b a car going round a bend on a flat, rough road
c the weight on the end of a swinging pendulum.
11 A car is travelling along a flat road. Explain why it cannot go around a bend if the road surface is perfectly smooth. Suggest what might happen if the driver tries turning the steering wheel.
Vector diagrams
Figure 17.9a shows an object travelling along a circular path, at two positions in its orbit. It reaches position B a short time after A. How has its velocity changed between these two positions?
The change in the velocity of the object can be determined using a vector triangle. The vector triangle in Figure 17.9b shows the difference between the final velocity vB and initial velocity vA. The change in the velocity of the object between the points B and A is shown by the smaller arrow labelled Δv. Note that the change in the velocity of the object is (more or less):
■■ at right angles to the velocity at A
■■ directed towards the centre of the circle.
The object is accelerating because its velocity changes. Since acceleration is the rate of change of velocity:
a = Δv Δt
a
b
vB
vA
vector representing change in velocity (Δv)
B A
gravitational Sun pull of Sun
Δv vB
vA
Figure 17.9 Changes in the velocity vector.
it follows that the acceleration of the object must be in the same direction as the change in the velocity – towards the centre of the circle. This is not surprising because, according to F = ma, the acceleration a of the object is in the same direction as the centripetal force F.
Acceleration at steady speed
Now that we know that the centripetal force F and acceleration are always at right angles to the object’s velocity, we can explain why its speed remains constant. If the force is to make the object change its speed, it must have a component in the direction of the object’s velocity; it must provide a push in the direction in which the object is already travelling. However, here we have a force at 90° to the velocity, so it has no component in the required direction. (Its component in the direction of the velocity is F cos 90° = 0.) It acts to pull the object around the circle, without ever making it speed up or slow down.
You can also use the idea of work done to show that the speed of the object moving in a circle remains the same. The work done by a force is equal to the product of the force and the distance moved by the object in the direction of the force. The distance moved by the object in the direction of the centripetal force is zero; hence the work done is zero.
If no work is done on the object, its kinetic energy must remain the same and hence its speed is unchanged.
QUESTION
12 An object follows a circular path at a steady speed. Describe how each of the following quantities changes as it follows this path: speed, velocity, kinetic energy, momentum, centripetal force, centripetal acceleration. (Refer to both magnitude and direction, as appropriate.)
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