16 Circular Motion

SI unit for angle is radian - which is the angle subtended by a circular arc with a length equal to the radius of the circle. Angle in radians = arc length/radius = 2πr/T = 2π radians.

Angular Velocity - is the rate of change of angle. ω = θ/T  ω = 2π/T ω = 2π/F.

Angular velocity is measured in several different units including degrees per second, revolutions per seconds, revolutions per minute or rads per second.

Frequency = 1/time period. 

There is a constant net force perpendicular to the velocity that causes the body to move in a circular motion. This is called the centripetal force. This force is often created by friction. 

This force has no component in the horizontal direction so no work is done in that direction.

Linear Velocity =2π x radius/Time   Linear Velocity = radius x ω 

Centripetal Acceleration - acceleration of any object travelling in a circular path at constant speed, towards the centre of the circle.

a = v^2/radius  a = ω ^2 x radius 

Centripetal Force

The object's speed remains constant because the component of the force acting on the object in the direction of motion is zero. 

F = ma   F = mv^2/radius  or F = mass x ω^2 x radius  

The force is always towards the centre of the circular path.

Investigating circular motion

Measurements that need to be taken: the mass of the bung and the weights. Weights = mass x gravity. Radius of the circle measured from the middle, and the time period calculated using a stopwatch. Repeat for different weights and plot a graph of ω^2 against force should be a straight line graph. When f = mg the object is travelling at circular motion. Centripetal force is greater than the weight downards,the object will then move up.