17 Motion In A Circle

Question 1

Circumference of the wheel

Answer 1

2πr

Question 2

Frequency of rotation

Answer 2

F=1/T

Question 3

Speed v of a point on the perimeter

Answer 3

V = 2πr / T

Question 4

Radians

Answer 4

360 = 2π

1 rad = 57.3

Question 5

Angular displacement

Answer 5

The angle an object in circular motion turns through. If its time period is T and its frequency is f, its angular displacement in the time t

2πft = 2πt / T

Question 6

Angular speed

Answer 6

The rate of change of angular displacement of an object in circular motion

Question 7

Centripetal force

Answer 7

The resultant force on an object that moves along a circular path. For the object of mass (m) moving at speed (v) along a circular path of radius (r) the centripetal force = mv^2 / r towards the centre of the circle

Question 8

Centripetal acceleration (equation)

Answer 8

A = v^2 / r

Question 9

Centripetal acceleration

Answer 9

For an object moving at a speed (v) in uniform circular motion, it centriptal acceleration towards the Centre of the circle

Question 10

For an object whirling around rapidly on the end of the string

Answer 10

The tension in the string provides most of the centripetal force

Question 11

For a satellite moving around the earth

Answer 11

The force of gravity between the satellite and the Earth is the centripetal

Question 12

For a planet moving around the sun

Answer 12

The force of gravity on the planet due to the sun is the centripetal force

Question 13

For the capsule on the London Eye

Answer 13

The centripetal force is the resultant of the support force on the capsule and the force of gravity on it

Question 14

Centripetal force (equation)

Answer 14

F = mv^2 / r

Question 15

Hint

Answer 15

1- if the object is acted on by a single force, that force is the centripetal force that causes the centripetal acceleration

2- the centripetal force is at right angles to the direction of the objects velocity. Therefore, no work is done by the centripetal force on the object because there is no displacement in the direction of the force. The kinetic energy of the object is therefore constant, so its speed is unchanged

Question 16

Over the top of the hill

Answer 16

mg -S = mv^2 / r

( the vehicle would lose contact with the road if its speed is equal to or greater than speed v0. If this happens the support force is zero)

Question 17

On a roundabout

Answer 17

Force of friction

F = mv^2 / r

( for no skidding or slipping to occur, the force of friction between the tyres and the road surface must be less than the limiting value that is proportional to the vehicles weight)

Question 18

Limiting force of friction

Answer 18

F0 = mv0^2 / r

Question 19

On a banked track

Answer 19

Without any banking the centripetal force on the road vehicle is provide only by sideways friction between the vehicle wheels and the road surface.

On a banked track the speed can be higher. There will be no sideways friction on the tyre from the road

Question 20

On a banked track (equation)

Answer 20

V^2 = grtan

Question 21

Big dipper

Answer 21

S = mg + mv^2 / r

Question 22

Very long swing

Answer 22

V^2 = 2gh

S-mg = mv^2 / L

Question 23

Big wheel

Answer 23

At maximum height, the reaction R from the wheel on each person acts downwards. So, the resultant force at this position is equal to mg + R. This reaction force and the weight provides the centripetal force. Therefore, at the highest position, if the wheel speed is v

R = mv^2 / r -mg

Question 24

Safe rides

Answer 24

Amusement rides are checked regularly to ensure they are safe. Accidents in the U.K. are investigated by the Heath and safety Executive. People can experience g-force different directions.

Question 25

Uniform circular motion

Answer 25

Motion of object moving at constant speed along a circular path