Question

A flywheel rotating about a fixed axis has a kinetic energy of \(500\) joule, if its angular frequency is \(5\) Hz, then calculate the moment of inertia of the wheel about the axis of rotation. (\(π^2 = 10\))

• A. \(0.6\text{ kg m}^2\)
• B. \(1\text{ kg m}^2\)
• C. \(0.75\text{ kg m}^2\)
• D. \(0.15\text{ kg m}^2\)

Hint:

Use $\omega=2\pi f$ and $K=\frac12I\omega^2$.

Answer 1

The Correct Option is B

Step 1: Find \(\omega\)
The frequency is \(5\) Hz, so \(\omega=2\pi\times5=10\pi\) rad/s.

Step 2: Use the energy formula
\(K=\frac12I\omega^2\), so \(500=\frac12I\times100\pi^2=50\pi^2I\).

Step 3: Solve
With \(\pi^2=10\): \(500=500I\), so \(I=1\) kg m\(^2\). Option (B).

Final Answer:
\(I=1\) kg m\(^2\), option (B). \[ \boxed{\text{(B) }1\text{ kg m}^2} \]