A flywheel is in the form of solid circular wheel of mass 72 kg and radius of 0.5 m and it takes 70 rpm, then the energy of revolution is

Options

A. 24 J
B. 2.4 J
C. 240 J
D. 2400 J

Explanation

To solve the problem of finding the energy of revolution of a flywheel, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values:**
- Mass (M) = 72 kg
- Radius (R) = 0.5 m
- Rotational speed (N) = 70 rpm

2. **Convert the rotational speed from rpm to revolutions per second (RPS):**
\[ \text{RPS} = \frac{N}{60} = \frac{70}{60} \approx 1.1667 \text{ RPS} \]

3. **Calculate the angular velocity (ω) in radians per second:**
\[ \omega = 2\pi \times \text{RPS} = 2\pi \times \frac{70}{60} = \frac{140\pi}{60} \approx 7.33 \text{ rad/s} \]

4. **Calculate the moment of inertia (I) for a solid circular wheel:**
\[ I = \frac{1}{2} M R^2 = \frac{1}{2} \times 72 \times (0.5)^2 = \frac{1}{2} \times 72 \times 0.25 = 9 \text{ kg m}^2 \]

5. **Calculate the kinetic energy (KE) of the flywheel:**
\[ KE = \frac{1}{2} I \omega^2 = \frac{1}{2} \times 9 \times (7.33)^2 \]
\[ KE = \frac{1}{2} \times 9 \times 53.7289 \approx 241.76 \text{ J} \]

6. **Round the kinetic energy to the nearest whole number:**
\[ KE \approx 242 \text{ J} \]

7. **Final answer:**
The energy of revolution of the flywheel is approximately **242 Joules**.