A fly wheel (disc form) of mass 50 kg and diameter 100 cm is making 150 revolutions/ min. What will be the angular momentum of flywheel?

Answer

To find the angular momentum of the flywheel, we will follow these steps:

### Step 1: Convert the angular velocity from revolutions per minute (rpm) to radians per second.
Given:
- Angular velocity (ω) = 150 revolutions/minute

To convert revolutions per minute to radians per second, we use the conversion factor:
\[ 1 \text{ revolution} = 2\pi \text{ radians} \]
\[ 1 \text{ minute} = 60 \text{ seconds} \]

Thus, the conversion is:
\[ \omega = 150 \, \text{rev/min} \times \frac{2\pi \, \text{rad}}{1 \, \text{rev}} \times \frac{1 \, \text{min}}{60 \, \text{s}} \]
Calculating this gives:
\[ \omega = 150 \times \frac{2\pi}{60} = 5\pi \, \text{rad/s} \]

### Step 2: Calculate the moment of inertia (I) of the flywheel.
The moment of inertia for a disc is given by the formula:
\[ I = \frac{1}{2} m r^2 \]
Where:
- \( m = 50 \, \text{kg} \) (mass of the flywheel)
- The diameter of the flywheel is 100 cm, hence the radius \( r \) is:
\[ r = \frac{100 \, \text{cm}}{2} = 50 \, \text{cm} = 0.5 \, \text{m} \]

Now substituting the values into the moment of inertia formula:
\[ I = \frac{1}{2} \times 50 \, \text{kg} \times (0.5 \, \text{m})^2 \]
Calculating this gives:
\[ I = \frac{1}{2} \times 50 \times 0.25 = \frac{50}{8} = 6.25 \, \text{kg m}^2 \]

### Step 3: Calculate the angular momentum (L) using the formula \( L = I \omega \).
Now we can calculate the angular momentum:
\[ L = I \omega = 6.25 \, \text{kg m}^2 \times 5\pi \, \text{rad/s} \]
Calculating this gives:
\[ L = 6.25 \times 5 \times 3.14 = 98.125 \, \text{kg m}^2/\text{s} \]

### Final Answer:
The angular momentum of the flywheel is approximately:
\[ L \approx 98.125 \, \text{kg m}^2/\text{s} \]

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