## Angular velocity

Angular velocity is given by,

$$\omega = \frac{d\theta}{dt}$$

## Angular displacement

Angular displacement is given by, $$\theta = \frac{s}{r}$$

## Angular acceleration

Angular accceleration is given by,

$$\alpha = \frac{d\omega}{dt}$$

SI unit of angular acceleration is rad s-2. Its dimensional formula is [M0L0T-2].

## Angular momentum

Angular momentum is given by $$\vec{L} = \vec{r} \times \vec{p}$$ Where $$\vec{p}$$ is linear momentum of the particle and $$\vec{r}$$ is position vector of the particle.

### Relation between torque and angular momentum

Relation between torque and angular momentum is given $$\tau = \frac{d\vec{L}}{dt}$$

## Tangential acceleration

Tangential acceleration is given by,
$$a_T = \vec{\alpha}\times\vec{r}$$

Where $$\vec{\alpha}$$ is the angular acceleration and $$\vec{r}$$ is the position vector.

## Centripetal acceleration

Centripetal acceleration is given by,
$$a_c = \vec{\omega}\times\vec{v}$$

Where $$\vec{\omega}$$ is the angular velocity and $$\vec{v}$$ is the linear velocity.

## Torque

If a force $$\vec{F}$$ acts at a point, whose position vector is $$\vec{r}$$; the torque due to force

$$\vec{\tau} = \vec{r} \times \vec{F}$$