A flywheel makes 240 revolutions per minute. What is the angular velocity expressed in radians?

1. Break Down the Problem

To find the angular velocity in radians, we need to convert revolutions per minute (RPM) to radians per second.

2. Relevant Concepts

• 1 revolution is equal to $2\pi$ radians.
• To convert from RPM to radians per second, we will use the formula: $\omega = \text{RPM} \times \frac{2\pi \, \text{radians}}{1 \, \text{revolution}} \times \frac{1 \, \text{minute}}{60 \, \text{seconds}}$ where $\omega$ represents angular velocity.

3. Analysis and Detail

1. Given that the flywheel makes 240 revolutions per minute: $\text{RPM} = 240$
2. Substitute RPM into the formula: $\omega = 240 \times \frac{2\pi}{1} \times \frac{1}{60}$

4. Verify and Summarize

Now we carry out the calculation: $\omega = 240 \times \frac{2\pi}{60}$ $\omega = 240 \times \frac{\pi}{30}$ $\omega = 8\pi \, \text{radians per second}$

Final Answer

The angular velocity of the flywheel is $8\pi$ radians per second.