Kinetic Energy of Rotating Body
Let us assume a body of Mass ‘m’ rotating with velocity v at a distance ‘r’ from the axis of rotation. Its angular velocity is then given by ω = v/r then v = rω. Now we know that the Kinetic Energy of a body is given by
KE = 1/2mv2
⇒ KE = 1/2m(rω)2
⇒ KE = 1/2mr2ω2
⇒ KE = 1/2Iω2
Hence, the Kinetic Energy of a Rotating Body is given by half of the product of the Moment of Inertia and the angular velocity of the body. The kinetic energy of rotating body is also called Rotational Kinetic Energy. The formula of Rotational Kinetic Energy is given as
KE = 1/2Iω2
The Moment of Inertia(I) is independent of the angular velocity of the body. It is a function of the mass of the rotating body and the distance of the body from the axis of rotation. Hence, we observe that angular motion is analogous to linear motion, this means that the significance of Moment of Inertia is that it gives an idea about how masses are distributed at different distances from the axis of rotation in a rotating body.
Moment of Inertia
Moment of inertia is the property of a body in rotational motion. Moment of Inertia is the property of the rotational bodies which tends to oppose the change in rotational motion of the body. It is similar to the inertia of any body in translational motion. Mathematically, the Moment of Inertia is given as the sum of the product of the mass of each particle and the square of the distance from the rotational axis. It is measured in the unit of kgm2.
Let’s learn about the Moment of Inertia in detail in the article below.
Table of Content
- Moment of Inertia Definition
- Moment of Inertia Formula
- Factors Affecting Moment of Inertia
- How to Calculate Moment Of Inertia?
- Moment Of Inertia Formula for Different Shapes
- Radius of Gyration
- Moment of Inertia Theorems
- Moments of Inertia for Different Objects