11.1.3

# Rotational Motion

Test yourself

## Rotational Motion

Rotational motion is described in a very similar way to linear motion.

### Angular displacement

• Angular displacement is the change in angle, θ, usually measured in radians.

### Angular velocity

• Angular velocity is the rate of change of angle with time, usually measured in radians per second.
• $\omega = \frac{\Delta \theta}{\Delta t}$

### Angular acceleration

• Angular acceleration is the rate of change of angular velocity, measured in radians per second per second.
• $\alpha = \frac{\Delta \omega}{\Delta t}$

## Angular acceleration

There is a set equations to find quantities under constant angular acceleration.

### Angular velocity

• The equation for angular velocity is:
• $\omega = \frac{\Delta\theta}{{\Delta}t}$
• Angular velocity can also be expressed in terms of linear velocity:
• $\omega = \frac{v}{r}$

### Angular acceleration

• Angular acceleration is the rate of change of angular velocity. The equation for angular acceleration is:
• Angular acceleration = change in angular velocity ÷ change in time
• $\alpha = \frac{\Delta\omega}{{\Delta}t}$
• Where $\alpha$ is the angular acceleration.

### Angular SUVAT equations

• There are angular versions of SUVAT equations which have the form:
• ${\omega_2}={\omega_1}+{\alpha}t$
• $\theta = {\omega_1}t+\frac{{\alpha}t^2}{2}$
• $\theta = \frac{({\omega_1}+{\omega_2})}{2}t$
• ${\omega_2}^2= {\omega_1}^2 + 2\alpha\theta$
• Where $\theta$ is the angular displacement.