# Radial Acceleration and Centripetal Force

## Objects travelling in a Circle

### This implies that any object that moves in a circle therefore must be experiencing an unbalanced Force, as shown in the diagram below :- ### This acceleration toward the centre of the circle is known as the Radial Acceleration and requires an inwards Force to cause it - the Centripetal Force. ### The time ( Δt ) can be found using the following formula :- ### The Change in Velocity ( Δv ) can be found by the following approximation :-  ### The Average Acceleration of the particle can then be found by the following :- ### The above formula gives the Acceleration over a large time period. If the value of θ is made to tend towards Zero, the value of sinθ ≈ θ and the Instantaneous Acceleration at a point can be found :-  ## Centripetal Force

### The Centripetal Force can be found mathematically by combining Newton's Second law with the Radial Acceleration :- ## Centripetal Force Case Study : Horizontal Circle

### A mass can be attached to the end of a string and rotated in a horizontal circle as shown in the diagram below :- ## Centripetal Force Case Study : Vertical Circle

### A mass can be attached to the end of a string and rotated in a vertical circle as shown in the diagram below :- ## Centripetal Force Case Study : Conical Pendulum

### As was seen in the horizontal circle case study above, Weight caused the object to follow the path shown in blue below :- ## Centripetal Force Case Study : Car on a Circular Track

### For a car moving on a circular track ( or around a roundabout ), the Centripetal Force is provided by the Frictional Force between tyres and the road. ## Centripetal Force Case Study : Car on a Banked Circular Track

### By changing the angle of the track, however, it is possible to achieve a higher speed than would be possible on the flat track. This is due to a component of the Reaction Force acting Centripetally :- 