Question

write Moment of Inertia as an Analogous Quantity for Mass​

Answer 1

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In XIth Std. we saw that angular displacement, angular velocity and angular acceleration respectively replace displacement, velocity and acceleration for various kinematical equations. Also, torque is an analogous quantity for force. Expressions of linear momentum, force (for a fixed mass) and kinetic energy include mass as a common term. In order to have their rotational analogues, we need a replacement for mass.

If we open a door (with hinges), we give a certain angular displacement to it. The efforts needed for this depend not only upon the mass of the door, but also upon the (perpendicular) distance from the axis of rotation, where we apply the force. Thus, the quantity analogous to mass includes not only the mass, but also takes care of the distance wise distribution of the mass around the axis of rotation. To know the exact relation, let us derive an expression for the rotational kinetic energy which is the sum of the translational kinetic energies of all the individual particles.

Answer 2

Explanation:

moment to 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 partical with its square of distance from the axis of rotation.