A system of large number of particles in which the distance between any two particles remains fix throughout the motion is called rigid body.

### Moment of inertia

Moment of inertia I is given by,

$$ I = \Sigma m_i r_i^2$$

### Torque

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

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

### Angular displacement

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

### Angular velocity

Angular velocity is given by,

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

### 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 [M

^{0}L

^{0}T

^{-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.