Mass of the sphere, m = 20 kg
Radius r = 0.25 m
Angular velocity 0 = 5 rad s^-1
Angular momentum \(L=I\omega =\frac{2}{5} mr^{2}\omega\)
\(=\frac{2}{5}\times 20 \times (0.25)^{2}\times 5 = 40 \times (0.0625)=2.5\)
L = 2.5 kg m² s^-1.

Mass of the electron, m = 9 \(\times\)10^-31 kg
Radius of the electron, r = 0.53 \(\overset { 0}{ A } \) = 0.53 \(\times\)10^-10 m
Velocity of the electron, v = 2.2 \(\times\)10⁶ ms^-1
Angular momentum of electron is, L = I\(\omega\)
Electron is considered as a point mass. Hence, its moment of inertia is, I= mr²
The relation, \(\omega=\frac{v}{r}\)could be used.
Angular momentum, \(L=mr^{2}\times \frac{v}{r}=mvr\)
=\(9.1 \times 10^{-31}\times 2.2 \times 10^{6}\times 0.53\times 10^{-10}\)
\(L=1.06\times 10^{-34}\)kg m² s^-1. 

The torque about the axis will rotate the object about it and the torque perpendicular to the axis will turn the axis of rotation when both exist simultaneously on a rigid body the body will have a precession.

A rigid body is the one which maintains its definite and fixed shape even when an external force acts on it.

\({x}_{CM}={m_1+m_2+m_2x_2\over m_1+m_2}={12\times0+16\times1.13 \over 12+16}=0.6457\ \mathring{A}\)

For symmetrically shaped bodies of uniform composition (Eg: spheres, cylinders, rectangular solids), the centre of mass is located at the geometrical centre of the body.

I_x = 3 \(\times\) (3)² + 4 \(\times\) (2)² = 43 unit
I_y = 2\(\times\) (2)² + 4 \(\times\) (2)² = 24 unit
I_z = 2 \(\times\) (2)² + 3 \(\times\) (3)² + 4 \(\times\) (\(\sqrt { 2 } \))²
= 8 + 27 + 32 = 67 unit

The line of action of normal force N exerted by the table on the block does not depend on h because the reactionary force N exerted by the table which is directed vertically upward and passes through its centre of gravity. Since the block is in equilibrium, N=mg.
Friction is always perpendicular to the normal force N acting between the surfaces. It acts tangential to the surface of contact.

Lifting a table from the floor by two persons. Pushing the car by two persons.

Due to the added weight of rice sack, centre of gravity of the combined body weight and the carrying weight shifted to new position. Once he bends, the Centre of gravity realigns as with the body's axis making his body balanced.

The weight of tree exerts a torque about the point where the cut is made. This causes rotation of the tree about the cut has to be made at say point A to weaken the tree trunk and to shift the centre of mass to the right and eventually move towards the ground on the right.

In the absence of external torque, the angular momentum of the rigid body or system of particles is conserved.
If \(\tau\) = 0 then, \(\frac { dL }{ dt } =0\) ; L= constant

(i) The torque of a force about an axis is independent of the choice of the origin as long as it is chosen on that axis itself.
(ii) Let O be the origin on the axis AB, which is the rotational axis of a rigid body. F is the force acting at the point P. Now, choose another point O' anywhere on the axis.
(iii) The torque of F about O' is,
\(\overset { \rightarrow }{ O'P } \times \overset { \rightarrow }{ F } =(\overset { \rightarrow }{ O'O } +\overset { \rightarrow }{ OP } )\times \overset { \rightarrow }{ F } \)
=\((\overset { \rightarrow }{ O'O } \times \overset { \rightarrow }{ F } )+(\overset { \rightarrow }{ OP } \times \overset { \rightarrow }{ F } )\)
(iv) As \(\overset { \rightarrow }{ O'O } \times \overset { \rightarrow }{ F } \)  is perpendicular to \(\overset { \rightarrow }{ O'O } \)  this term will not have a component along AB. Thus, the component of \(\overset { \rightarrow }{ O'P } \times \overset { \rightarrow }{ F } \)  is equal to that of \(\overset { \rightarrow }{ OP } \times \overset { \rightarrow }{ F } \).

The direction of torque is found using right hand rule. This rule says that if fingers of right hand are kept along the position vector with palm facing the direction of the force and when the fingers are curled the thumb points to the direction of the torque.

A point mass is a hypothetical point particle which has nonzero mass and no size or shape.