find the angular velocity in radians per second for 157 rpm

To find the angular velocity in radians per second (rad/s) for 157 revolutions per minute (RPM), we can use the following conversion formula:

\[
\text{Angular Velocity} (\omega) = \text{RPM} \times \frac{2\pi \text{ radians}}{1 \text{ revolution}} \times \frac{1 \text{ minute}}{60 \text{ seconds}}
\]

Substituting 157 RPM:

\[
\omega = 157 \times \frac{2\pi}{60}
\]

Now, let's calculate it.

\[
\omega = \frac{314\pi}{60} \approx 16.44 \, \text{rad/s}
\]

So, the angular velocity is approximately **16.44 radians per second**.

Would you like further explanation or have any other questions?

### Related Questions:
1. What is the angular velocity in degrees per second for 157 RPM?
2. How is angular velocity related to linear velocity?
3. What is the period (time for one full revolution) for 157 RPM?
4. How does RPM affect the centripetal force on a rotating object?
5. How can you calculate angular displacement from angular velocity?

### Tip:
Angular velocity is directly proportional to RPM, so increasing RPM increases the angular velocity at the same rate.

Learn how to find the angular velocity in radians per second for 157 RPM using the formula ω = RPM × (2π/60). The solution walks through step-by-step conversion from revolutions per minute to radians per second, with the final answer approximately 16.44 rad/s. Perfect for high school students studying trigonometry and angular motion.

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