Q.1. Write the formula for moment of inertia in the terms of radius of gyration. Write its S.I.
Answers
The moment of inertia of a body about an axis is sometimes represented using the radius of gyration. Now, what do you mean by the radius of gyration? We can define the radius of gyration as the imaginary distance from the centroid at which the area of cross-section is imagined to be focused at a point in order to obtain the same moment of inertia. It is denoted by k.
Radius of Gyration Formula
The formula of moment inertia in terms of the radius of gyration is given as follows:
I = mk2 (1)
where I is the moment of inertia and m is the mass of the body
Accordingly, the radius of gyration is given as follows
\(k=\sqrt{\frac{I}{m}}\) (2)
The unit of the radius of gyration is mm. By knowing the radius of gyration, one can find the moment of inertia of any complex body equation (1) without any hassle.
Consider a body having n number of particles each having a mass of m. Let the perpendicular distance from the axis of rotation be given by r1, r2, r3,…,rn. We know that the moment of inertia in terms of radius of gyration is given by the equation (1). Substituting the values in the equation, we get the moment of inertia of the body as follows
Answer:
Moment of inertia angular mass or rotational interia can be defined w.r.t. rotation axis, as a quality that decides the amount of torque required for a desired angular acceleration or a property of a body due to which it resists angular acceleration. The formula for moment of inertia is the " sum of the product of mass " of each particles with the " square of its distance from the axis of the rotation" The formula of moment of inertia is expressed as I = €mi ri^2.