# Rotational Motion

## Basic Definitions

#### Angular Motion

**Angular motion**, or **rotational motion**, is the movement of an object which is rotating around an axis.

#### Angular Displacement

**Angular displacement** ( **angle through which the object rotates**, measured in **radians** (

#### Angular Velocity

**Angular velocity** ( **rate of change of angular displacement**, measured in **radians per second** (

#### Angular Acceleration

**Angular acceleration** ( **rate of change of angular velocity**, measured in **radians per second squared** (

Don't confuse

#### Linear Velocity

**Linear velocity** or **tangential velocity** ( **instantaneous linear velocity** of a rotating object - it is the velocity of an object revolving around an axis if the tether breaks.

#### Linear Acceleration

**Linear acceleration** or **tangential acceleration** ( **instantaneous linear acceleration** of a rotating object - it's the **change in tangential velocity**.

#### Radial Acceleration

**Radial acceleration** ( **acceleration towards the centre** of a rotating system, caused by centripetal force.

is the **radial acceleration**, in metres per second squared.is the **radius**of the rotating system, in metres.is the **angular velocity**, in radians per second.is the **linear velocity**, in metres per second.

## Equations of Motion

The equations of motion **can be applied to angular motion** as well as linear motion, as long as all tangential/linear quantities are substituted for their angular counterparts.

Quantity | Linear | Angular |
---|---|---|

Displacement | ||

Initial Velocity | ||

Current Velocity | ||

Acceleration | ||

Time (doesn't change!) |

You can convert between **linear** and **angular** motion by **multiplying or dividing the radius** as a factor. To think about this intuitively, this is because