In physics, the moment of inertia is a quantitative measure of a body's rotational inertia— that is, the opposition the body exhibits to having its rotational speed around an axis altered by applying torque. The axis can be internal or external and can be fixed or not. However, in relation to that axis, The moment of inertia (I) is always specified and defined as the sum of the products obtained by multiplying the mass of each particle of matter within a given body by the square of its distance from the axis. In measuring angular momentum for a rigid body the moment of inertia is equivalent to the mass at linear momentum. The force p represents the mass m times the linear momentum velocity v; whereas for angular momentum, the angular momentum L is equal to the moment of inertia I times the angular velocity.
The figure shows two balls of steel that are welded to a rod AB connected to a bar OQ at C. Neglecting the mass of AB and assuming all particles of the mass m of each ball are concentrated at a distance r from OQ, I= 2mr2 gives the moment of inertia.
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Dimensional Formula of Moment of Inertia
Moment of inertia is defined as the mass product and the square of the spinning radius
Moment of Inertia = Mass x (Radius of Gyration)2
Dimensional Formula of Mass= (M1L0T0)
Dimensional Formula of Radius of Gyration= (M0L1T0)
(Radius of Gyration)2=M0 L2 T0
Substituting these values in the above equation we get
Dimensional formula for moment of inertia= M1L2T0
SI unit of Moment of Inertia is kg m²