Circular Motion

The angle subtended by a circular arc with a length equal to the radius of the circle (approximately 57.3^o)

angle in radians = arc length / radius

.

For a complete circle, arc length = circumference

∴ angle in radians = 2πr / r = 2π radians

The rate of change of angle for an object moving in a circular path

ω = θ / t

ω = 2π / T

ω = 2πf as f = 1 / T

Direction continuously changing

Velocity continuously changing, even if speed constant

Acceleration

↑ rate of change of velociy = ↑ acceleration

• A force that keeps an object moving with a constant speed in a circular path

.

• 'Centre-seeking'

.

• Arises when weight and normal contact force interact with each other

.

• Perpendicular to velocity

.....∴ Force has no component in direction of motion

.....∴ No work done on object

.....∴ Speed remains constant

v = 2πr / T

v = rω as ω = 2π / T

The acceleration of an object moving in a circular path with a constant speed, which always acts towards the centre of the circle

a = v² / r

a = ω²r

F = mv² / r

F = mω²r

...

Stationary: weight = normal contact force

.

Moving: net force required in order for an object to move in a circular path

Top

• Normal contact force decreases
• Net force downwards towards centre of circle
• Weight decreases slightly

Bottom

• Normal contact force increases
• Net force upwards towards centre of circle
• Weight increases slightly