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 [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 $$\tau = \frac{d\vec{L}}{dt}$$

Ta…

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 [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 $$\tau = \frac{d\vec{L}}{dt}$$

Ta…