Chapter 17 Motion in a circle
17.1 Uniform circular motion
An object rotating at a steady rate is said to be in uniform circular motion
The circumference of the circle = 2 x pi x frequency
The frequency of rotation = 1 / T
The velocity of a point on the perimeter = 2 x pi x radius / T
Angular displacement and angular speed
The angular displacement, theta = 2 x pi x f x t
The angular speed, w = 2 x pi x f
17.2 Centripetal acceleration
its centripetal acceleration, a = v.2 / r
The resultant force on an object around a circle at a constant speed is called the centripetal force because it acts in the same direction as the centripetal acceleration, which is towards the centre of the circle.
Equation for centripetal
centripetal force, F = m x w.2 x r
17.3 On the road
Over the top of the hill
mg - S = m x v.2 / r
Where S is the support force, mg is the weight of the car, v is the velocity that the car is going at the point of measuring and r is the radius of the curvature of the hill
On a roundabout
force of friction, F= m x v.2 / r
For no skidding to occur, the force of friction between the tyres and the road surface must be less than a limiting value, F0, that is proportional to the vehicles weight. Therefore for no slipping to occur the velocity must be below a particular value v0.
limiting force of friction, F0 = m x v0.2 / r
On a banked track
Without any banking, the centripetal force on a road vehicle is provided only by sideways friction between the vehicle wheels and the road surface
There is no sideways friction if v.2 = g x r x tan theta
17.4 At the fairground