Motion in a Circle

Question 1

An angle of 2π rad is equal to ______ degrees.

Answer 1

360 degrees

Question 2

Define the radian.

Answer 2

One radian is the angle subtended at the centre of a circle by an arc equal in length to the radius.

Question 3

What is angular displacement θ?

Answer 3

A measure of the angle through which an object moves in a circle.

Question 4

Define angular velocity ω.

Answer 4

The rate at which the angular displacement changes.

Question 5

An object is moving along a circle of radius r with angular velocity ω.
Its linear speed v = ________

Answer 5

v = rω

Question 6

Direction of centripetal force?

Answer 6

Centripetal force is directed towards the centre of the circle.
Centripetal force is perpendicular to the velocity of the object.

Question 7

Formulae for centripetal acceleration

Answer 7

a = v^2/r

a = rω^2

Question 8

Formulae for centripetal force.

Answer 8

F = ma

F = mv^2/r

F = mrω^2

Question 9

The centripetal force changes the direction of the velocity but the magnitude of the velocity is constant. Why?

Answer 9

This is because the centripetal force is always perpendicular to the direction of the velocity.
Since work done = force x distance moved in the direction of the force, the work done by the centripetal force is 0.
According to the work-energy theorem, the kinetic energy and the speed of the object will therefore remain constant.

Question 10

Moon orbiting the Earth:

Centripetal force is provided by ________ .

Answer 10

gravitational force.

Question 11

A car cornering on a flat, rough road:

Centripetal force is provided by ______.

Answer 11

frictional force acting on tyres.

Question 12

A stone tied to a string, and spun in a horizontal circle:

Centripetal force is provided by ______ .

Answer 12

First, sketch a diagram of the forces.

Answer: Tension in the string acting on the stone.