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MCQs: Circular motion

Fill in the missing words with words from this list: acceleration   speed   centre  first   unbalanced   constant   perpendicular   velocity   work 

The ball has constant  but, because its direction is changing, its  is not constant. This means that it has   : according to Newton's  law there must be an  force acting on the ball. The kinetic energy of the ball is  so no  is done on the ball. This means that the force must be  to the direction of motion, in other words towards the   .

Speed, kinetic energy and work done are scalar quantities. Velocity, acceleration and force are vector quantities.

A 4 kg green ball completes a circle of radius 1 m in 2 s.

The centripetal force is:

\(F = mω^2r = 4 \times (2π/2)^2\times 1 = 4π^2\) N

A 2 kg red ball attached to a string is made to move in a circle as shown.

If the tension in the string is 23.1 N, the centripetal force is:

Centripetal force = horizontal component of tension = 23.1 sin 30 = 11.6 N

A ball on a string is moved in a circle so fast that the string breaks.

The direction of the balls motion when the string breaks is:

Ball will move with tangential velocity.

A ball on a string is made to swing as shown

The tension at the bottom of the swing is

The ball is moving in a part of a circle so at the bottom its is accelerating upwards. The upward force, T, is therefore greater than the downward force, W.

This is a tricky one since when we derive the equation for a pendulum we assume the forces are balanced. This is approximation is only applicable if the amplitude is small. The amplitude in this question isn't small enough.

A red ball moves in a circle of radius 2 m at a constant speed of 4 ms-1.

The time for one revolution is:

Distance travelled in one revolution = circumference = 2πr = 2π x 2 = 4π
time = distance/speed = 4π/4

A 2kg blue ball moves in a circule of radius 4 m at a constant speed of 2 ms-1.

The centripetal force is: 

\(F = {mv^2\over r} = {2 \times 2^2\over4} = 2\) N

A ladybird stands on a rotating record (maybe some of you have seen these contraptions that we used to play music on).

The force that holds the ladybird in a circle is

Normal force and weight act perpendicular to the surface; only friction acts towards the centre.

A cyclist rides around a banked frictionless track as shown.

The centripetal force is provided by a component of:

Only normal force has a component towards the centre.

A ball is made to move around the sides of a circular bowl as shown.

As always, the centripetal force is towards the centre.

A red ball moves in a vertical circle on the end of a string as shown.

As the ball goes around the circle:

Applying Newton's 2nd law at the bottom: \(ma = T - mg\) so \(T = ma + mg\)

At the top: \(ma = mg -T\) so \(T = mg - ma\)

Total Score:

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