Question

A flywheel rotating about a fixed axis has a kinetic energy of 360 J when its angular speed is 30 rads^-1. The moment of inertia of the wheel about the axis of rotation is

• A. 0.6 kgm²
• B. 0.15 kgm²
• C. 0.8 kgm²
• D. 0.75 kgm²

Hint:

Flywheel rotating about a fixed axis works on the principle of conservation of angular momentum, to store rotational energy. 

Answer 1

The Correct Option is C

Flywheel rotating about a fixed axis works on the principle of conservation of angular momentum, to store rotational energy. 

The kinetic energy of the flywheel = 360 J, angular speed, ω = 30 rad/s

The relation between kinetic energy, angular speed, and moment of inertia is as follows.

K.E. = ½ Iω²

• Where I = moment of inertia 
• ω = angular speed

Putting the values in the formula, we get 

360 = ½ I(30)²

Simplifying the expression.

\(I = \dfrac{2 \times 360}{900} = 0.8kg{m^2}\)

So, the moment of inertia of the wheel is 0.8 kgm² when its kinetic energy is 360 Joules.

Hence, the correct option is (C) is 0.8 kgm².

Answer 2

Kinetic Energy =  ½ Iω²

\(I=\frac{2K.E}{\omega^2}=\frac{2 \times 360}{30 \times 30}=0.8 \,kgm^2\)

A flywheel rotating about a fixed axis has a kinetic energy of 360 J when its angular speed is 30 rads^-1. The moment of inertia of the wheel about the axis of rotation is 0.8 kgm².

Note: Flywheel is used to supply continuous power in systems where the energy source is not continuous. The moment of inertia is an angular analogue of inertia defined by Newton’s first law of motion. In angular motion, an object shows resistance to change in its state of motion or rest which is called the moment of inertia.

• All the laws of motion valid for uniform linear motion are also valid for uniform angular motion.
• A flywheel provides continuous pulses of energy at power levels, more than the ability of the source of its energy.

Answer 3

The moment of Inertia is given by the product of mass and the square of the radius. 

I = MR²

To calculate I - 

\(E=\dfrac{1}{2}Iω^2\)

Given - ω = 30 rad/s

Rotational kinetic energy, E = 360 J

Assuming that the moment of inertia of the flywheel as we know from the relation between Kinetic energy and moment of Inertia as follows:

Rotational kinetic energy: = \(E=\dfrac{1}{2}Iω2\)

Putting the given values from above in this equation, we have,

\(360=\dfrac{1}{2}I(30)^{2}\)

\(I=\dfrac{360×2}{30^{2}}\)

\(I=0.8kgm^2\)

Hence, the value of the moment of Inertia of the flywheel is \(0.8kgm^{2}\).

So, the correct answer is “Option C”.