No, it may lie outside the body. In case of semicircular ring, it is at the centre which is outside the ring.

Friction with the surface.

When the girl carries a bag in her left hand, the centre of gravity of the system is shifted to the left. In order to bring it in the middle, the girl has to lean towards right.

The point of contact of the ladder with the ground is the point about which the ladder can rotate. When the labourer is at the top of the ladder, the lever arm of force i large. So, the turning effect can. be large.

Yes, a particle in translatory motion always has an angular momentum, unless the point (about which angular momentum is calculated) lies on the line of motion.

Only rotational motion

The radial component of a force does not contribute towards torque.

No, \(K=\sqrt { \frac { 1 }{ M } } \)

Angular momentum of a body is measured with respect to certain origin.

So, a body in translatory motion can have angular momentum.
It will be zero, if origin lies on the line of motion of particle.

1.9 km-m/s

The moment of inertia \(\left( I=\frac { 1 }{ 2 } MR^{ 2 } \right) \) of the earth about its own axis will become one-fourth and so its angular velocity will become four times\(\left( L=I\omega =constant \right) \). Hence, the time period will reduce to one-fourth \(\left( T=2\pi /\omega \right) \), i.e. 6 hours.

M = 20 Kg, \(\omega =100rad/s,R=0.25m\).
Moment of inertia of cylinder about its own axis
\(=\frac { 1 }{ 2 } MR^{ 2 }=\frac { 1 }{ 2 } \times 20\times { \left( 0.25 \right) }^{ 2 }\)    
Rotational KE \(=\frac { 1 }{ 2 } { I\omega }^{ 2 }\) 
 \(=\frac { 1 }{ 2 } { I\omega }^{ 2 }=\frac { 1 }{ 2 } \times 0.625\times { \left( 100 \right) }^{ 2 }=3125J\).

Molten ice from poles into ocean and so mass is going away from axis of rotation. So, moment of inertia of earth increases and to conserve angular momentum, angular velocity (\(\omega \)) decreases. So, time period of rotation increases (\(T=2\pi /\omega \) ). So, net effect of global warming is increasing in the duration of day.

The moment of inertia of the system (circular table + two boys) decreases. To conserve angular momentum (\(L=I\omega =constant\)), the speed of rotation of the circular table increases.

When the person withdraws his chest, his moment of inertia decreases. No external torque is acting on the system. So, to conserve angular momentum, the angular velocity increases.