Dimensions of Moment of Inertia

Introduction

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

Now,

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

FAQs (Frequently Asked Questions)

1. What is the Dimensional Formula for Inertia?

It is an extensive (additive) property: The moment of inertia for a point mass is simply the mass times the square of the perpendicular distance to the rotation axis.

2. How is the Moment of Inertia Calculated?

Basically, for any rotating object, it is possible to calculate the moment of inertia by taking the distance of each particle from the axis of rotation (r in the equation), squaring that value (that is the r² term), and multiplying it by the mass of that particular.

3. What is the SI Unit of Inertia?

Inertia moment is defined as the tendency of an object to remain in a state of rest or constant rotational velocity. More the moment of inertia needs more torque to alter this condition. In rotational motion, torque plays the same role in linear motion as power. Its SI unit is kg. metre².

4. What is the Difference Between Inertia and Moment of Inertia?

But inertia implies only the body's location, whether it's in motion or at rest. Moment of inertia is the object's measure of resistance to rotation w.r.t an axis, also referred to as the "Second Moment of Mass / Area," it varies from axis to axis of the same organism.