c) What is moment of inertia? How is it defined (write an equation, explaining all the terms) ? What is the parallel axis principle for moment of inertia? (if the moment of inertia for a body is I for rotation about an axis that passes through its center of mass, what will be the moment of inertia, Ip, for rotation parallel to that axis? Explain the terms you use in the equation

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Explanation:

What is moment of inertia?

Mathematically Moment of Inertia I = Mr²

where m = mass of the body

r = distance of body to the rotattinal axis

This is a quantity expressing a body's tendency to resist angular acceleration, which is the sum of the products of the mass of each particle in the body with the square of its distance from the axis of rotation.

What is the parallel axis principle for moment of inertia?

The theorem of parallel axis states that the moment of inertia of a body about an axis parallel to an axis passing through the centre of mass is equal to the sum of the moment of inertia of body about an axis passing through centre of mass and product of mass and square of the distance between the two axes.

(if the moment of inertia for a body is I for rotation about an axis that passes through its center of mass, what will be the moment of inertia, Ip, for rotation parallel to that axis?

Ip = I + Mα²

Explain the terms you use in the equation

where, α is the distance between two axes (also called the radius of gyration)

I is more moment of inertia about the centre of mass

Ip is the momont of inertia of the rotation parallel to the axis that passes through the centre of mass

M is the mass of the body