If a flywheel makes `120" rev"//"min"`, then its angular speed will be

Options

A. `8 pi" rad"//s`
B. `6 pi" rad"//s`
C. `4 pi" rad"//s`
D. `2 pi" rad"//s`

Answer

To find the angular speed of a flywheel that makes 120 revolutions per minute, we can follow these steps:

### Step 1: Understand the relationship between revolutions and angular speed
Angular speed (ω) is related to the number of revolutions per unit time. The formula for angular speed in terms of frequency (ν) is given by:
\[ \omega = 2\pi \nu \]
where:
- \( \omega \) is the angular speed in radians per second,
- \( \nu \) is the frequency in revolutions per second.

### Step 2: Convert revolutions per minute to revolutions per second
The flywheel makes 120 revolutions per minute. To convert this to revolutions per second, we divide by 60 (since there are 60 seconds in a minute):
\[ \nu = \frac{120 \text{ rev/min}}{60 \text{ s/min}} = 2 \text{ rev/s} \]

### Step 3: Substitute the frequency into the angular speed formula
Now that we have the frequency in revolutions per second, we can substitute it into the angular speed formula:
\[ \omega = 2\pi \nu = 2\pi \times 2 \text{ rad/s} \]

### Step 4: Calculate the angular speed
Now, we can perform the multiplication:
\[ \omega = 4\pi \text{ rad/s} \]

### Conclusion
The angular speed of the flywheel is:
\[ \omega = 4\pi \text{ rad/s} \]