Question

A flywheel rotating about a fixed axis has a kinetic energy of $360J$ when its angular speed is $30ra{d^{ - 1}}$. The moment of inertia of the wheel about the axis rotation is:
A. $0.6kg{m^2}$
B. $0.15kg{m^2}$
C. $0.8kg{m^2}$
D. $0.75kg{m^2}$

Answer 1

Flywheel rotating about a fixed axis works on the principle of conservation of angular momentum, to store rotational energy. This rotational energy is analog to linear kinetic energy. This is used to store the energy in large energy storage systems.

Complete step by step solution:
The kinetic energy of the flywheel $KE = 360J$, angular speed $\omega = 30ra{d^{ - 1}}$
We have the following relation between kinetic energy, angular speed, and moment of inertia.
$KE = \dfrac{1}{2}I{\omega ^2}$
Here, $I$ is the moment of inertia and $\omega$ is the angular speed.
Let us put the values in the above formula.
$360 = \dfrac{1}{2}I{\left( {30} \right)^2}$
Let us simplify the expression.
$I = \dfrac{{2 \times 360}}{{900}} = 0.8kg{m^3}$
So, the moment of inertia of the wheel is $0.8kg{m^3}$ when its kinetic energy is $360$ joules.
Hence, the correct option is (C) is $0.8kg{m^2}$.

Note:
Flywheel is also used to supply continuous power outs in systems where the energy source is not continuous.
The moment of inertia is an angular analog of inertia defined by Newton’s first law of motion. As in linear motion, an object resists the change in its state of motion or rest, in angular motion also the object shows this resistance which is called the moment of inertia.
All the laws of motion which are valid for uniform linear motion are also valid for uniform angular motion.
A flywheel is used to provide continuous pulses of energy at power levels. This is more than the ability of the source of its energy.