The number of revolutions made by a flywheel change from 300 rpm to 1500 rpm in 10 s. Calculate angular acceleration assuming it to be uniform. Also calculate the number of revoluations made during the time.

Explanation

To solve the problem, we will follow these steps:

### Step 1: Convert the initial and final angular velocities from RPM to radians per second.
1. **Initial angular velocity (ω₀)**:
\[ ω₀ = 300 \text{ rpm} = 300 \times \frac{2\pi \text{ rad}}{60 \text{ s}} = 10\pi \text{ rad/s} \]

2. **Final angular velocity (ω)**:
\[ ω = 1500 \text{ rpm} = 1500 \times \frac{2\pi \text{ rad}}{60 \text{ s}} = 50\pi \text{ rad/s} \]

### Step 2: Calculate the angular acceleration (α).
Using the formula for angular acceleration:
\[ α = \frac{ω - ω₀}{t} \]
where \(t = 10 \text{ s}\).

Substituting the values:
\[ α = \frac{50\pi - 10\pi}{10} = \frac{40\pi}{10} = 4\pi \text{ rad/s}^2 \]

### Step 3: Calculate the total angle (θ) covered during the time interval.
Using the formula:
\[ θ = ω₀ t + \frac{1}{2} α t^2 \]
Substituting the known values:
\[ θ = (10\pi)(10) + \frac{1}{2}(4\pi)(10^2) \]
Calculating each term:
\[ θ = 100\pi + \frac{1}{2}(4\pi)(100) = 100\pi + 200\pi = 300\pi \text{ rad} \]

### Step 4: Calculate the number of revolutions (n) made during the time.
The number of revolutions is given by:
\[ n = \frac{θ}{2\pi} \]
Substituting the value of θ:
\[ n = \frac{300\pi}{2\pi} = 150 \]

### Final Answers:
- **Angular acceleration (α)**: \(4\pi \text{ rad/s}^2\)
- **Number of revolutions (n)**: \(150\)