Find the centre of mass of a uniform $\left(a\right)$ half-disc, $\left(b\right)$ quarter-disc.

Two discs of moments of inertia $I_1$ and $I_2$ about their respective axes (normal to
the disc and passing through the centre), and rotating with angular speed $\omega 1$ and $\omega 2$ are brought into contact face to face with their axes of rotation coincident.

Does the law of conservation of angular momentum apply to the situation? why?

Two discs of moments of inertia $I_1$ and $I_2$ about their respective axes (normal to
the disc and passing through the centre), and rotating with angular speed $\omega 1$ and $\omega 2$ are brought into contact face to face with their axes of rotation coincident.

Find the angular speed of the two-disc system.

Two discs of moments of inertia $I_1$ and $I_2$ about their respective axes (normal to
the disc and passing through the centre), and rotating with angular speed $\omega 1$ and $\omega 2$ are brought into contact face to face with their axes of rotation coincident.

Calculate the loss in kinetic energy of the system in the process.

Two discs of moments of inertia $I_1$ and $I_2$ about their respective axes (normal to
the disc and passing through the centre), and rotating with angular speed $\omega 1$ and $\omega 2$ are brought into contact face to face with their axes of rotation coincident.

Account for this loss.

A disc of radius $R$ is rotating with an angular speed ${\omega }_0$ about a horizontal axis. It is placed on a horizontal table. The coefficient of kinetic friction is ${\mu }_k$.

What was the velocity of its centre of mass before being brought in contact with the table?

A disc of radius $R$ is rotating with an angular speed ${\omega }_0$ about a horizontal axis. It is placed on a horizontal table. The coefficient of kinetic friction is ${\mu }_k$.

What happens to the linear velocity of a point on its rim when placed in contact with the table?

A disc of radius $R$ is rotating with an angular speed ${\omega }_0$ about a horizontal axis. It is placed on a horizontal table. The coefficient of kinetic friction is ${\mu }_k$.

What happens to the linear speed of the centre of mass when disc is placed in contact with the table?

A disc of radius $R$ is rotating with an angular speed ${\omega }_0$ about a horizontal axis. It is placed on a horizontal table. The coefficient of kinetic friction is ${\mu }_k$.

Which force is responsible for the effects in $\left(b\right)$ and $\left(c\right)$.