- A-Level Physics

# Circular Motion, SHM & Oscillations

The S.I. unit for angles is not degrees, but **radians**. This is the angle subtended by a circular arc with a length equal to the radius of the circle:

**1 rad is equal to about 57.3°**

**There are 2****π in a circle,** and half that in a semicircle. Therefore,

to convert from degrees to radians, divide the angle in degrees by 180/π

to convert from radians to degrees, multiply the angle in radians by 180/π

## Circular Motion

While the velocity of linear motion is defined as displacement / time, the velocity of circular motion is defined as angle / time. Therefore, it is called **angular velocity**, and is given the Greek letter omega, ω.

ω = θ/tangular velocity = angle / time

This equation is rarely used, however, as it is far easier to work with the time period and frequency of circular motion.

**Time period, T,**is the time taken for it to complete one circle.**Frequency, f,**refers to the number of complete rotations (of 2π rads) per second.

This gives rise to the far more helpful equations:

ω= 2π/T angular velocity = 2π / time period

ω= 2πf angular velocity = 2π x frequency

**The units of angular velocity are radians per second.**

We can calculate the linear velocity using the angular velocity:

v =ωrlinear velocity = angular velocity x radius

### Centripetal Force

Even if the object undergoing circular motion is travelling at a constant speed, its **velocity is always changing** (due to its direction changing). This means the object is always accelerating – this is known as **centripetal acceleration, and always acts towards the centre of the circle.**

a = v²/r centripetal acceleration = linear velocity² / radius

a =ω²r centripetal acceleration = angular velocity² x radius