Question

describe application in real life for moment inertia in ( thin rod) and (hoop or cylindrical shell) and ( circular disc or cylinder) and (sphere) and (spherical shell) ?

Answer 1

To explain the applications in real life of moment of inertia, first, we have to understand the basic definition of the moment of inertia, which is as follows:

Moment of Inertia (MOI): It is basically a physical quantity for a body and this physical quantity is a rotational analogue of the mass of the body and thus it also defines the resistance of the body to angular acceleration about a given axis. In other words, it also describes the ease for a body to rotate about a given axis.

In simple words, one can also define the moment of inertia as characteristic of a rotating body due to which it opposes the change in its condition of rest or rotational motion. Also, the moment of inertia is a scalar quantity and has no direction

In general, MOI is denoted as "I" and the mathematical expression of a moment of inertia of a particle of mass "m" rotating with radius "r" can be written as

  

However, in a system of particles, there are more than one particles, thus to calculate the moment of inertia of a system of particles, we simply add the moment of inertia of all particles of a body. suppose, we have a system having three particles with masses m1, m2 and m3 are rotating with radii r1, r2 and r3 respectively and image can be seen as follows:

Now the moment of inertia for this body is calculated as:

Therefore, one can say that the moment of inertia depends upon mass distribution.

Now thin rod, hoop or cylindrical shell, circular disc or cylinder, sphere, spherical shell are different bodies with a different number of particles. Therefore, their moment of inertia will be calculated accordingly.

In this question, our main focus is to define the applications of the moment of inertial for above-mentioned bodies.

• Firstly let's explain the thin rod.

A falling chimney is a good example describing the moment of inertia of thin rod.

Next, a description of the moment of inertial for a hoop is as follows:

Next, the uniform disc is described:

Bike wheels are very good example real-life example of uniform disc moment of inertia. Because to change the angular velocity of the wheel. Also, the plain merry-go-round is a good example of a uniform disc moment of inertia.