A ball moves along the inside of a horizontal semi-circular ring as shown. The diagram is a view from above.

Which arrow represents the direction of the average force on the ball?

B. The average force is toward the center.

For a particle moving at constant speed in a horizontal circle, the work done by the centripetal force is

A. zero.

B. directly proportional to the particle mass.

C. directly proportional to the particle speed.

D. directly proportional to the (particle speed)^{2}

A. zero because the particle is at a constant speed

A car moves from X to Y along a semicircular path. The radius of the path is 250m and the time taken to complete the trip is 50s. Which of the following correctly shows the magnitude of the average velocity and the magnitude of the average speed?

Average Velocity Average Speed

A. 10 ms^{-1} 10 ms^{-1}

B. 10 ms^{-1 } 10 ms^{-1}

C. 16 ms^{-1 } 10 ms^{-1}

D. 16 ms^{-1} 16 ms^{-1}

B

A particle P is moving anti-clockwise with constant speed in a horizontal circle. Which diagram correctly shows the direction of the velocity v and acceleration a of the particle P in

the position shown?

C

A brick is placed on the surface of a flat horizontal disc as shown in the diagram below. The disc is rotating at constant speed about a vertical axis through its centre. The brick does not move relative to

the disc.

D

A communications satellite is moving at a constant speed in a circular orbit around Earth. At any given instant in time, the resultant force on the satellite is

A. zero.

B. equal to the gravitational force on the satellite.

C. equal to the vector sum of the gravitational force on the satellite and the centripetal force.

D. equal to the force exerted by the satellite’s rockets.

B. equal to the gravitational force on the satellite

The Moon orbits the Earth. Which of the following diagrams correctly represents the force(s) acting on the Moon?

A

A particle moves in a circular path of radius r. The magnitude of the force acting on the particle is F. The work done by the force in one complete orbit of the particle is

A. 2πFr.

B. F/2π

C. 2π/F

D. zero.

D

The Moon orbits the Earth in a nearly circular orbit at constant speed as shown. Which of the following diagrams correctly shows the force(s) acting on the Moon in the position shown above?

B

A ball is swinging in a horizontal circle as shown in the diagram below. Which one of the following diagrams best shows the forces acting on the ball when it is at the position shown above?

C

Two satellites of equal mass, S_{1} and S_{2}, orbit the Earth. S_{1} is orbiting at a distance r from the Earth’s centre at speed v. S2 orbits at a distance 2r from the Earth’s centre at speed 2/(v)^{1/2}. The ratio of th centripetal force on S_{1} to the centripetal force on S_{2} is

A. 1/8

B. 1/4

C. 4

D. 8

C

The centripetal force F acting on a particle of mass m that is travelling with linear speed v along the arc of a circle of radius r is given by

A. F= v^{2}/mr

B. F= mv^{2}r

C. F= mr^{2}v

D. F= mv^{2}/r

D. the centripetal force is equal to the mass times velocity squared all divided by the radius

A point mass is moving in a horizontal circle with a velocity of constant magnitude v. At one particular time, the mass is at P. A short time later, the mass is at Q, as shown below. Which vector diagram correctly shows the change in velocity ∆v of the mass during this time?

C

Which of the following diagrams represents the direction of the centripetal force F acting on a car travelling in a circular path?

B

Two points P and Q are at distances r and 2r respectively from the centre of a compact disc (CD) as shown. When the disc is rotating about its centre, the ratio of the acceleration at P/acceleration at Q

is

A. 1/2

B. 1

C. 2^{1/2}

D. 2

A

Points P and Q are at distances R and 2R respectively from the centre X of a disc, as shown below. The disc is rotating about an axis through X, normal to the plane of the disc. Point P has linear speed

v and centripetal acceleration a. Which one of the following is correct for point Q?

linear speed centripetal acceleration

A. v a

B. v 2a

C. 2v 2a

D. 2v 4a

C

A particle is moving around the circumference of a horizontal circle of radius r with constant speed v. Which of the following is the acceleration of the particle?

A.v^{2}/r towards the centre of the circle

B.v^{2}/r away from the centre of the circle

C. v^{2}r towards the centre of the circle

D. v^{2}r away from the centre of the circle

A

In a fairground ride, a car of mass M travels on rails around a vertical loop of effective radius R. At the top of the loop, the speed of the car is v. The car stays in contact with the rails, as shown below. The acceleration of free fall is g. Which of the following is the correct expression for the force that the rails exert on the car?

A. (Mv^{2}/R)- Mg

B. Mv^{2}/R

C. Mg

D. (Mv^{2}/R)+ Mg

A. the force is equal to the mass times velocity squared all divided by the radius all subtracted by the mass times gravity