How fast will the wheel spin in revolutions per minute?  

To convert the angular velocity from radians per second to revolutions per minute (RPM), we'll follow these steps:

1. **Find the angular velocity in revolutions per second:**

   We already found that the angular velocity \( \omega \) is \( \frac{15}{8} \) radians per second.

   Since \( 1 \) revolution is equal to \( 2\pi \) radians, we convert the angular velocity to revolutions per second:

   \[
   \text{Angular velocity in revolutions per second} = \frac{\omega}{2\pi} = \frac{\frac{15}{8}}{2\pi} = \frac{15}{16\pi} \text{ revolutions per second}
   \]

2. **Convert revolutions per second to revolutions per minute:**

   There are 60 seconds in a minute, so:

   \[
   \text{RPM} = \frac{15}{16\pi} \times 60 = \frac{900}{16\pi} \text{ revolutions per minute}
   \]

So, the wheel spins at \( \frac{900}{16\pi} \) revolutions per minute.

Would you like more details or have any questions?

Here are 5 related questions:
1. How many seconds would it take for the wheel to complete one revolution?
2. If the radius of the wheel doubled, what would be the new RPM?
3. How does the linear speed of the hamster affect the RPM of the wheel?
4. What would the RPM be if the hamster slowed down to 10 cm/s?
5. How would the angular velocity change if the wheel were spinning twice as fast?

**Tip:** Converting between units often involves multiplying by conversion factors, so keep common conversions like \( 2\pi \) radians per revolution and 60 seconds per minute in mind.

Learn how to convert angular velocity from radians per second to revolutions per minute (RPM). This detailed explanation covers the conversion process step-by-step, including unit conversions and calculations. Suitable for high school students and beyond.

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