EXERCISES

For a thin flat circular disc, the radius of gyration about a diameter as axis is $k$. If the disc is cut along a diameter $AB$ as shown into two equal pieces, then find the radius of gyration of each piece about $AB$.

Two uniform circular discs, each of mass $1 \mathrm{kg}$ and radius $20 \mathrm{cm}$, are kept in contact. Find the moment of inertia of the system of two discs about the tangent passing through their point of contact.

Four spheres each diameter $2 a$ and mass $\text{'}m\text{'}$ are placed with their centres on the four corners of a square of the side $b$. Calculate the moment of inertia of the system about any side of the square.

A metre stick is balanced on a knife edge at its centre. When two coins, each of mass $5 \mathrm{g}$ are put on top of the other at the $12.0 \mathrm{cm}$ mark, the stick is found to be balanced at $45.0 \mathrm{cm}$. What is the mass of the metre stick?

Determine the kinetic energy of a circular disk rotating with a speed of $60 \mathrm{rpm}$ about an axis passing through a point on its circumference and perpendicular to its plane. The circular disk has a mass of $5 \mathrm{kg}$ and radius $1 \mathrm{m}$.

Two particles, each of mass $m$ and speed $u$, travel in opposite directions along parallel lines separated by a distance $d$. Show that the vector angular momentum of the two particle system is the same whatever be the point about which the angular momentum is taken.

The moment of inertia of a flywheel making $300$ revolutions per minute is $0.3 {\mathrm{kgm}}^2$. Find the torque required to bring it to rest in $20 \mathrm{s}$.

When $100 \mathrm{J}$ of work is done on a flywheel, its angular velocity is increased from $60 \mathrm{rpm}$ to $180 \mathrm{rpm}$. What is the moment of inertia of the wheel?