Circular Motion

What is a circular motion ?

• Motion along a circular path / arc.

Uniform Circular Motion

• Circular motion with constant speed.

Non-uniform Circular Motion

• Circular motion with changing speed

Circular Motion … Examples

– Earth moving around the Sun– Electron moving around a proton in a

hydrogen atom.– Moving car in a roundabout.– Simple pendulum.

Circular Motion … Periodic Motion

distance = rate time

time =distance

rate v

T =2 r

v

2

r

Periodic Motion :Motion that repeat itself after a fixed time.

Period : Time of one “cycle”.

Is the ball accelerating ?

When the string breaks . . .

The string breaks at this position

The object then moves along a straight line.

Without tension the object moves in a straight line.

Tension changes the direction of the object.

Circular Motion … Accelerating Motion

• Object moves along a circular path.• The direction of velocity is changing.• Changing velocity implies that the object accelerates.

Magnitude :

Centripetal Acceleration

rr

va 2

2

Direction : Towards the centre

Q: Is the acceleration a constant?

Centripetal Acceleration . . . Proof

s vv

v

rt

r

tv

r

s

r

v

t

v

dt

dva

2

Centripetal Acceleration . . . Proof

s

90

2

180 limφ lim

2

180φ

0Δθ0Δθ

F ma

Fmv

r

2

Centripetal Force

Centripetal Force

• When an object moves in a circle, it must accelerates.• The acceleration directs toward the centre of the circle.• According to Newton’s 2nd law, there has to be a force

to produce such acceleration• This force must point toward the centre of the circle

(Centripetal Force)

Origin of Centripetal Force

Circular Motion Centripetal Force

Satellite in orbit around Earth Gravitational force of the Earth

Car moving around a flat-curve Static frictional force

Car moving around a banked-exitStatic frictional force and normal force

Toy-plane tied to a rope and moving in a circle

Tension in the rope

Astronaut in a rotating space station

Normal force by the surface/floor

Rider at a roller coaster weight and/or normal force