Question

What are the units of moment of inertia? Of angular speed $\mathit{\omega }$? Of angular momentum? Of linear momentum?

Short answer

The unit of moment of Inertia is$\mathrm{kg}.{\mathrm{m}}^2$

The unit of angular speed is rad/s

The unit of angular momentum is$\mathrm{kg}.{\mathrm{m}}^2/\mathrm{s}$

The unit of Linear momentum is kg.m/s

Step-by-step solution

Definition of Moment of Inertia, Angular speed, Angular Momentum and Linear Momentum.

The moment of inertia is a quantitative measure of a body's rotational inertia—that is, the body's resistance to having its speed of rotation along an axis changed by the application of a torque (turning force).

The rate of change of angular displacement is known as angular speed.

The rotating inertia of an object or system of objects in motion about an axis that may or may not pass through the object or system is described by angular momentum.

Linear Momentum is the momentum of translation, which is a vector quantity equal to the product of mass and velocity of the center of mass in classical physics.

Unit of Moment of Inertia and the unit of Angular speed

The moment of inertia of the disk of mass M and radius r is

$I=M{r}^2$

Here unit of mass is kg unit of radius is meter (m) Therefore the unit of moment of inertia is$\mathrm{kg}.{\mathrm{m}}^2$

The unit of angular speed is rad/s

Unit of Angular momentum and the unit of Linear Momentum

The angular momentum of the system with moment of inertia and velocity can be expressed as

$L=I\omega$

Here unit of moment of inertia is $\mathrm{kg}.{\mathrm{m}}^2$and unit of angular speed is rad/s

By combining these units, we get unit of angular momentum as$\mathrm{kg}.{\mathrm{m}}^2/\mathrm{s}$

The linear momentum of the body of mass moving with speed v can be expressed as

p=mv

Here the unit of mass is kg and unit of speed is m/s

By combining these units, we get of linear momentum as kg.m/s

Hence, the unit of Moment of Inertia, Angular speed, Angular Momentum and Linear Momentum is $\mathrm{kg}.{\mathrm{m}}^2,\mathrm{rad}/\mathrm{s},\mathrm{kg}.{\mathrm{m}}^{2/}\mathrm{s}\mathrm{and}\mathrm{kg}.\mathrm{m}/\mathrm{s}$respectively.