Question

What happens when moment of inertia increases?

Answer 1

1. Moment of 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 particle with its square of a distance from the axis of rotation.
2. It can be described as a quantity that decides the amount of torque needed for a specific angular acceleration in a rotational axis.
3. The moment of inertia is usually specified with respect to a chosen axis of rotation.
4. The general mathematical form of moment of inertia is
   $$\begin{gathered} \mathrm{Moment}\mathrm{of}\mathrm{inertia}=\mathrm{mass}\mathrm{of}\mathrm{the}\mathrm{body}\times {\left(\mathrm{distance}\mathrm{from}\mathrm{the}\mathrm{axis}\mathrm{of}\mathrm{the}\mathrm{rotation}\right)}^2 \\ \mathrm{I}={\mathrm{mr}}^2 \end{gathered}$$
5. As the moment of inertia increases, the speed of rotation decreases.
6. When the moment of inertia increases angular velocity decreases.
7. When mass moves from the axis of rotation, i.e. difficult to change rotational velocity.