Moment of Inertia Rectangle

Moment of Inertia Rectangle:

 In this blog we are going to learn Moment of Inertia Rectangle.But before that we should know the Inertia difinition  .

Inertia is the inability of a body to change by itself either the state of rest or of uniform motion along a straight line unless an external force is applied on it.

Now let's dicuss about moment of inertia and Moment of Inertia Rectangle.I believe that this concept will halp you to understand moment of inertia cylinder concept also.

You can see a wheel and a uniform disc with the same mass rotating about a same axis.

Why is it difficult to start or stop the wheel than to start or stop the disc even though both of them have same mass?

This is because the force required to start or stop an object undergoing rotational motion depends on the product of the mass of the object and the square of the distance from the axis of rotation to the particles which make up the body.

The product of mass and square of the distance from the axis of rotation is greater in the case of a wheel.

This explains why it is difficult to start or stop a wheel. 

The product of mass of the particle and the square of the distance of the particle from the axis of rotation gives the moment of inertia.

Moment of inertia of a body = m₁r₁ + m₂r₂ + ……….+ m_nr_n.Where m_1,  m₂……….m_n are the masses of the particles constituting the object and r₁, r₂……..r_n are the distances of these particles from the axis of rotation. (To be read as - m₁r₁ + m₂r₂ till m_nr_n)

The equation can also be written as

Where m is the mass of the particle and r is the distance of the particle from the axis of rotation.

The SI unit of moment of inertia is kilogram meter squared and the dimensional formula is ML².

The moment of inertia of a rectangle shape such as this one is easily calculated by using the equation I = 1/12 bh3.

Using this equation we can solve  inertia of a rectangular problems.