Motion In A Circle

> An object rotating at a steady rate is in uniform circular motion.

The circumference of a wheel = 2πr

The frequency of the rotation, f = 1/T

> Period, T - Time for one rotation

The speed of rotation, v = 2πr / T or v = 2πrf

> Angular displacement, θ

> The angular displacement in radians is calculated by:

θ = 2πt / T = 2πft

> Angular Speed, ω

ω = angular displacement / t

ω = 2π / T = 2πf

> The unit of ω is (rad s־ ¹)

> In an object moving in a circular motion at a constant speed, it's velocity, v, is

constantly changing direction. Since the velocity is changing direction the object is

accelerating.

> Acceleration - the change of velocity per second

> Centripetal - towards the centre of the circle

Centripetal acceleration, a = v² / r

> The resultant force on an object moving in a circular motion at a constant speed is referred to as the centripetal force as it acts in the same direction as the centripetal acceleration.

Examples of centripetal force

> An object spinning on a bit of string - Tension in the string

> A satellite orbiting the earth - Gravity pulling the satellite towards the earth

> For an object moving at a constant speed, v in a circular motion of radius, r

Centripetal force, f = mv² / r

Centripetal force, f = mω²r

2.3 On the road AQA Pg. 26

2.4 At the fairground AQA Pg. 28