Moment of Inertia of a System of Particles
Moment of Inertia of a system of particles is given by the formula,
I = ∑mi ri2
where,
ri is the perpendicular distance of the ith particle from the axis
mi is the mass of ith particle
The above Moment of Inertia equation tells that moment of inertia for a system of particles is equal to the sum of product of the mass of each and the square of the distance from the rotation axis of each particle.
For the figure given below,
Moment of inertia of first particle = m1×r12
Moment of inertia of second particle = m2×r22
Moment of inertia of third particle = m3×r32
Similarly,
Moment of inertia of nth particle = mn×rn2
Now the moment of inertia of the entire body about the axis of rotation AB will be equal to the sum of the moment of inertia of all the particles, so
I = m1×r12 + m2×r22 + m3×r32 +……+mn×rn2
I = Σ mi×ri2
where,
I represent moment of inertia of the body about the axis of rotation
mi is the mass of ith particle,
ri is the radius of ith particle
Σ represents the sum.
From the equation, we can say that the moment of inertia of a body about a fixed axis is equal to the sum of the product of the mass of each particle of that body and the square of its perpendicular distance from the fixed axis.
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