Question

To calculate moment of inertia of axis passing through centre of a square 

Answer 1

Momemt of inertia :-Moment of inertia is defined as the quantity expressed by the body resisting angular acceleration which is the sum of the product of the mass of every particle with its square of a distance from the axis of rotation. Or in more simple terms, it can be described as a quantity that decides the amount of torque needed for a specific angular acceleration in a rotational axis. Moment of Inertia is also known as the angular mass or rotational inertia. The SI unit of moment of inertia is kg m2.

 

The perpendicular distance of every particle from the given line is a/√2. The moment of inertia of one particle is M/(a/√2)^2=1/2ma^2

Since the square have four sides so the moment of inertia along the 4 side lines passing through its diagonal ,so the overall.moment of inertia is 

4×1/2Ma^2=2ma^2

So the moment of inertia at centre of the square is = 1/2ma^2

This is square with side a so along diagonal=a/√2

Momemt of inertia = I× Mr^2

I- radius of gyration m- mass of object 

 

 

There are 4 axis passing through centre of square so the common point of all axis is the centre of square steps to solve problem 

1)- solve the moment of inertia of one particle along the diagonal of square 

2)multiplied the result by 4