A flywheel rotates about a fixed axis and slows down from 400 rpm to 200 rpm in one minute How many revolutions does the flywheel complete in the same time ?

Options

A. 200 rev
B. 400 rev
C. 300 rev
D. 500 rev

Explanation

To solve the problem of how many revolutions a flywheel completes while slowing down from 400 rpm to 200 rpm in one minute, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Data:**
- Initial angular velocity, \( \omega_i = 400 \) rpm
- Final angular velocity, \( \omega_f = 200 \) rpm
- Time, \( t = 1 \) minute

2. **Convert Time to Seconds (if necessary):**
- Since we are working in revolutions per minute (rpm), we can keep the time in minutes for this calculation. However, if we were to convert it to seconds, we would have \( t = 60 \) seconds.

3. **Calculate Angular Deceleration (α):**
- We can use the formula:
\[ \omega_f = \omega_i + \alpha t \]
- Rearranging gives:
\[ \alpha = \frac{\omega_f - \omega_i}{t} \]
- Substituting the values:
\[ \alpha = \frac{200 \, \text{rpm} - 400 \, \text{rpm}}{1 \, \text{min}} = \frac{-200 \, \text{rpm}}{1 \, \text{min}} = -200 \, \text{rpm/min} \]

4. **Calculate the Total Revolutions (θ):**
- We can use the formula for angular displacement:
\[ \theta = \omega_i t + \frac{1}{2} \alpha t^2 \]
- Substituting the values:
\[ \theta = 400 \, \text{rpm} \times 1 \, \text{min} + \frac{1}{2} \times (-200 \, \text{rpm/min}) \times (1 \, \text{min})^2 \]
- Calculating each term:
\[ \theta = 400 \, \text{revolutions} - 100 \, \text{revolutions} = 300 \, \text{revolutions} \]

5. **Final Answer:**
- The flywheel completes **300 revolutions** while slowing down from 400 rpm to 200 rpm in one minute.