Question

The angular speed of a flywheel making 120 revolutions/minute is

• A. 4 $ \pi$ rad/s
• B. 4 $ \pi^2 $ rad/s
• C. $\pi$ rad/s
• D. 2 $ \pi $ rad/s

Answer 1

The Correct Option is A

To find the angular speed of a flywheel making 120 revolutions per minute (rpm), we need to convert this rate into radians per second (rad/s).

Step-by-step Explanation:

1. First, understand the relationship between revolutions and radians: One complete revolution is equivalent to \(2\pi\) radians.

   1 \text{ revolution} = 2\pi \text{ radians}

2. Next, convert the given revolutions per minute to revolutions per second:

   120 \text{ revolutions/minute} = \frac{120 \text{ revolutions}}{60 \text{ seconds}} = 2 \text{ revolutions/second}

3. Convert revolutions per second to radians per second using the relationship from step 1:

   2 \text{ revolutions/second} = 2 \times 2\pi \text{ radians/second}

   = 4\pi \text{ radians/second}

Conclusion: The angular speed of the flywheel is 4\pi rad/s.

The correct option is 4 \pi rad/s.