moving in circles

Moving in Circles

What forces are on you when

you go around a corner?

Task

• Try and explain why a car skids when it goes around a corner too quickly.

Learning objectives• How can we recognise uniform motion in a

circle?

• What do we need to measure to find the speed of an object moving in uniform circular motion?

• What is meant by angular displacement and angular speed?

Objects which move in a circular path any suggestions?

The hammer swung by a hammer thrower

Clothes being dried in a spin drier

Chemicals being separated in a centrifuge

Cornering in a car or on a bike

A stone being whirled round on a string

A plane looping the loop

A DVD, CD or record spinning on its turntable

Satellites moving in orbits around the Earth A planet orbiting the Sun (almost circular orbit for many)

Many fairground rides An electron in orbit about a nucleus

The Wheel

The speed of the perimeter of each wheel is the same as the cyclists speed, provide that the wheel does not slip or skid.

r

If the cyclists speed remains constant, his wheels turn at a steady rate. An object turning at a steady rate is said to be in uniform circular motion

The circumference of the wheel = 2 π r

The frequency of rotation f = 1/T, T is the time for 1 rotation

The speed v of a point on the perimeter = circumference/ time for 1 rotation

V = (2 π r) / T = 2 π r f

Worked example p22

Angular displacementThe big wheel has a diameter of 130m and a full rotation takes 30 minutes (1800 seconds)

3600 / 1800 = 0.20 per second (2π radians)

20 in 10 seconds

200 in 100 seconds (π/18 radians)

900 in 450 seconds (π/2 radians)

The wheel will turn through an angle of (2 π/T) radians per second

T is the time for one complete rotation

The angular displacement (in radians) of the object in time t is therefore = 2 π t T

= 2 π f t

The angular speed (w) is defined as the angular displacement / time

w = 2 π f w is measured in radians per second (rad s-1)