A flywheel rotates about a fixed axis and slows down from 200 rpm to 100 rpm in one minute. How many revolution does the wheel complete in one minute?

Options

A. 50
B. 100
C. 150
D. 200

Explanation

To solve the problem of how many revolutions a flywheel completes while slowing down from 200 rpm to 100 rpm in one minute, we can follow these steps:

### Step 1: Identify the given values
- Initial angular velocity, \( \omega_0 = 200 \) rpm
- Final angular velocity, \( \omega = 100 \) rpm
- Time, \( t = 1 \) minute

### Step 2: Convert time to consistent units
Since the angular velocities are given in revolutions per minute (rpm), we can keep the time in minutes. Therefore, we will use \( t = 1 \) minute directly.

### Step 3: Calculate angular acceleration (\( \alpha \))
We can use the formula:
\[ \omega = \omega_0 + \alpha t \]
Rearranging the formula to solve for \( \alpha \):
\[ \alpha = \frac{\omega - \omega_0}{t} \]
Substituting the known values:
\[ \alpha = \frac{100 - 200}{1} = -100 \text{ rpm}^2 \]

### Step 4: Calculate the total number of revolutions (\( \theta \))
We can use the angular displacement formula:
\[ \theta = \omega_0 t + \frac{1}{2} \alpha t^2 \]
Substituting the known values:
\[ \theta = 200 \times 1 + \frac{1}{2} \times (-100) \times (1)^2 \]
Calculating each part:
\[ \theta = 200 - 50 = 150 \text{ revolutions} \]

### Final Answer
The flywheel completes **150 revolutions** in one minute.

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