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

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