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### What is the moment of inertia?

Energy is necessary for the moving of stationary objects. Likewise, when a stationary object rotates, it also needs energy. To obtain that energy, we need a physical quantity that represents the difficulty of rotating the object relative to the axis of rotation. To obtain that energy, we need a physical quantity that represents the difficulty of rotating the object relative to the axis of rotation. This difficulty of rotation is called the **moment of inertia**. While the physical quantity representing the difficulty of moving the object with respect to the force is “mass”, the rotating version thereof is “moment of inertia”.

This moment of inertia \(I_ {j}\) is to be written

$$I_j=m_{j}r_{j}^{2}$$

where the distance from the mass point \(m_ {j}\) to the rotation axis stands for \(r_ {j}\).

All objects can be regarded as a mass of mass. Therefore, we can obtain the moment of inertia \(I\) of any object by integrating the above expression as the integral range of the whole object.

Furthermore, by using this moment of inertia \(I\) and the angular velocity \(ω\) of the rigid body, it is possible to express the kinetic energy \(K\) of rotation of the object.

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

You can remember this formula easily by comparing the above equation about \(K\) with the below equation about the kinetic energy E that you know.

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

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