Rotational Motion and Astrophysics 2

Question 1

Explain why the force of gravity does not pull a motorcyclist off the wall of a ball.

Answer 1

There is a centripetal force causing the motorcycle to move in a circle. If this force is greater than the gravitational pull downwards it will continue to push against the wheels of the motorcycle which will thus remain in contact with the wheel of death.

Question 2

Explain why water leaves a dogs coat when it shakes

Answer 2

As the water is not fixed to the coat it will continue with its linear velocity in a straight line as the coat shakes.

Question 3

At a certain speed, a toy car cannot go around a flat bend and breaks free of the track. Explain why this happens.
The flat track is replaced by a banked track with the same radius of curvature. The car is now able to travel safely around the bend at the same speed as before.

Answer 3

The centripetal force is no longer large enough to maintain the car’s circular motion
The centripetal force is now larger so can maintain the car’s circular motion.

Question 4

An ice skater begins to spin with his arms outstretched. He then pulls them in towards his body. State the effect this will have on:

(a) his moment of inertia;
(b) his angular velocity;
(c) his angular momentum.

Answer 4

(a) Decreases.
(b) Increases.
(c) Stays the same

Question 5

A flywheel is replaced by one of the same mass but the mass is concentrated near the rim of the flywheel. State the effect this will have on the time it takes for the flywheel to slow down if it starts from the same angular velocity as before and experiences the same frictional forces. You must provide justification for your answer

Answer 5

The flywheel will take longer to slow down. The moment of inertia will be greater the angular acceleration will be less. Thus the time taken to slow down will be greater.

Question 6

A motorcyclist leans her motorcycle over as she rides around a bend.
State the source of the centripetal force which causes the motorcyclist to turn

Answer 6

Friction between the tyre and the road

Question 7

A motorcyclist hits a patch of diesel which has spilt on the road. This reduces the friction between the motorcycle tyres and the road surface. Explain the effect this would have on the motorcycle as it rounds the bend.

Answer 7

Friction between tyre and road is now less so the centripetal force is reduced. This means that the outward forces on the tyre no exceed the centripetal force and the tyre slides outwards towards the outside of the bend.

Question 8

When an aircraft is banked it loses altitude. explain why this is the case.

Answer 8

When in level flight the lift provided by the wings balances the weight of the plane. When banked the lift provided by the wings is split into two components. These are the centripetal force and the upwards component to balance the weight of the aircraft. As the upwards force is now smaller than the weight of the plane it will lose altitude.

Question 9

State the principle of conservation of angular momentum

Answer 9

Angular momentum is conserved when two or more bodies collide in the absence of external torque.

Question 10

Newton’s law is an inverse square law. Explain what this sentence means

Answer 10

An inverse square law means that the quantity being measured, in this case the force between two objects, is inversely proportional to the square of the distance between the objects.

Question 11

Define what is meant by the term ‘gravitational field strength’

Answer 11

Gravitational field strength at a point is defined as the force per unit mass at that point.

Question 12

Explain why the Moon has a greater influence on the tides than the Sun

Answer 12

The Moon has a greater influence because tides are caused by the difference in gravitational force across the Earth. The Earth’s diameter is such a small proportion of the Sun to Earth distance compared to the Moon to Earth distance that the Moon exerts the greatest influence.

Question 13

What causes the extra high tides known as spring tides

Answer 13

When the Sun and Moon are in direct alignment the gravitational forces are at their strongest creating the largest bulge in the oceans.

Question 14

Define what is meant by the term ‘gravitational potential’

Answer 14

Gravitational potential at a point in space is defined as the work done by external forces to move unit mass from infinity to that point

Question 15

Explain what is meant by the term ‘escape velocity’

Answer 15

Escape velocity is the minimum velocity required to just escape from a planet’s gravitational field and reach infinity with zero velocity.

Question 16

Frames of reference can be either accelerating or non-accelerating. Which of these is termed inertial and which is termed non-inertial?

Answer 16

Accelerating is non-inertial and non-accelerating is termed inertial

Question 17

Explain what is meant by the ‘equivalence principle’

Answer 17

The equivalence principle states that gravity pulling in one direction is equivalent to acceleration in the other. There is no way of distinguishing between the effects on an observer of a uniform gravitational field and of a constant acceleration

Question 18

A long spaceship is accelerating.

Does time run more slowly at the front or the rear of the spaceship?

Answer 18

At the rear of the spaceship

Question 19

What effect has altitude on the passage of time?

Answer 19

Time runs faster at higher altitudes.

Question 20

According to Einstein, what does a large mass do to space time?

Answer 20

It causes a warping of space time, the larger the mass the more the curvature of space time

Question 21

Describe the evidence for space time warping.

Answer 21

Gravitational time dilation  the less gravity there is, the faster time passes. A clock on board an orbiting satellite goes faster than a clock on the Earth’s surface.

Gravitational lensing  if an object has sufficient mass it can cause light which is travelling in a straight line to bend. This is one of the ways in which black holes are detected.

Precession of Mercury’s orbit  Mercury has an elliptical path around the Sun but it shifts slightly with each orbit. However the amount predicted by Newtonian mechanics is only half of that actually observed. The precession fits in perfectly with that predicted by Einstein taking general relativity into account.

Question 22

World lines describe the position of an object in 4 dimensions. What is the fourth dimension?

Answer 22

Time

Question 23

Define what is meant by a ‘black hole’

Answer 23

A black hole is an object where gravity is so great that noting can escape its gravitational pull. Its escape velocity is greater than the speed of light

Question 24

How is a black hole formed?

Answer 24

Black holes are created when a very big star collapses