what is moment of inertia and why do we calculate it?

Answer 1

Moment of inertia is important for rotational dynamics and kinematics problems. It's a way of taking a weighted average of an object's mass, by multiplying each mass by the square of its radial distance from an axis of rotation, and it represents the rotational inertia in the same way that mass represents linear inertia. For collections of point masses that are rigidly connected, this can be done discreetly by summing the finite values for mr^2. For extended solid objects, it is done by integration, and moment of inertia for standard shapes can be found in tables. For example, a sphere of mass m and radius r has a moment of inertia of (2/5)mr^2 about its diameter, a hollow cylinder of mass m and radius r (assuming an ideally thin wall) has a moment of inertia of mr^2 about its axis, and a solid cylinder has a moment of inertia of (1/2)mr^2 about its axis.

In a rotational physics problem, moment of inertia, I, replaces mass in many familiar formulas. For example, F = ma becomes T = Iα, where T is torque and α is angular acceleration. And while linear kinetic energy is 0.5*mv^2, rotational kinetic energy is 0.5*Iω^2, where ω is angular velocity.

Answer 2

There is also area moment of inertia, which is used to determine the stress and strain of parts in bending.