# ‘Moment of inertia’ of various shapes

• You can click various shapes on the left and right sides of the screen.
• What are the characteristics of a shape with a large moment of inertia?
• What are the characteristics of a shape with a small moment of inertia?

## rotational kinetic energy

All moving objects have energy. This motion includes not only linear motion, but also rotational motion.
The linear kinetic energy of an object is proportional to the object’s ‘mass‘ and the ‘square of its speed‘.

$E = \frac{1}{2}mv^{2}$

$$m$$: mass ($$kg$$)
$$v$$: speed ($$m/s$$)

The rotational kinetic energy of an object is proportional to the ‘moment of inertia‘ and the ‘square of the angular velocity.’

$E = \frac{1}{2}I\omega^{2}$

$$I$$: moment of inertia ($$kg·m^{2}$$)
$$\omega$$: angular velocity ($$rad/s$$)

If you look at the energy equations for linear motion and rotational motion, you can see that they are similar. That is, the mass ‘$$m$$’ in linear motion corresponds to the moment of inertia ‘$$I$$’ in rotational motion. And, the speed ‘$$v$$’ in linear motion corresponds to the angular velocity ‘$$\omega$$’ in rotational motion.

## Moment of inertia ‘$$I$$’

If ‘inertia’ is a property of maintaining motion in a linear motion. And the moment of inertia is a physical quantity that indicates the degree to which rotational motion is maintained in rotational motion.
In other words, a rotating object will continue to rotate if no external force is applied.

Inertia is proportional to the mass of an object, whereas the moment of inertia is influenced by the shape of the object and the mass.
Here are the moments of inertia for different shaped objects.