Circular motion

Angular velocity
Angular velocity ω is the size of angle an object rotates through per second. It can be considered similar to linear velocity as the time taken for an object to travel through an angular displacement

measured in rad s-1

Angular velocity can be converted into linear velocity,  ,using the equation:

with being the radius of the circle

Since  it can be rearranged to give angular velocity in terms of linear velocity

Frequency and Time period
frequency is the number of revolutions per second and time period is the time for one complete revolution. The two are linked by the equation

Since one complete revolution is 2π radians the time period can be calculated

Centripetal Force
Centripetal force is the net force that acts on an object moving in circular motion. The centripetal force always towards the centre of the circle and it is calculated using the equation:

An example of the centripetal force:

"R" being the Reaction force and "w" being the weight

Banked Turns
Resolved Horizontally

Nsin

Resolved vertically

Centripetal Acceleration
The object has moved around the circle in time  and has a chance of velocity of, represented by the vector diagram. Acceleration can then be calculated as

since the direction of is towards the centre of the circle, so is a