**Rigid body; Degrees of freedom, Euler’s theorem, angular velocity, angular momentum, moments of inertia, theorems of parallel and perpendicular axes,**

Questions:

**Q 1. **A homogeneous right triangular pyramid wih the base side $a$ and height $\frac32a$ **is **shown below. Obtain the moment of inertia tensor of the pyramid. **[15 marks]**

**Q 2. **The angular momentum $\vec M$ of a rigid body comprising of N particles and rotating with angular velocity $\vec \omega$ is given by $\vec M = \displaystyle\sum_{k=1}^N m_k \vec r_k \times (\vec \omega \times \vec {r_k})$ , where the origin coincides with the centre of mass. Express the components of $\vec M$ in terms of components of the inertia tensor. Hence, show that the most general free rotation of a spherical top is a uniform rotation about an axis fixed in space. **[15 marks]**

Video Solution: