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

To find the moment of inertia of the flywheel, we can use the formula for rotational kinetic energy given by:

K.E. = \frac{1}{2} I \omega^2

where K.E. is the kinetic energy, I is the moment of inertia, and \omega is the angular speed.

We are given:

• Kinetic Energy, K.E. = 360 \, \text{J}
• Angular Speed, \omega = 30 \, \text{rads}^{-1}

We need to find the moment of inertia I. Substituting the known values into the equation:

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

This simplifies to:

360 = \frac{1}{2} I \times 900

Which further simplifies to:

360 = 450 I

Solving for I, we divide both sides by 450:

I = \frac{360}{450} = \frac{4}{5} = 0.8 \, \text{kgm}^2

Thus, the moment of inertia of the flywheel is 0.8 \, \text{kgm}^2, which matches option 0.8 kgm².