Math Problem Statement

find the angular velocity in radians per second for 157 rpm

Solution

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

Angular Velocity(ω)=RPM×2π radians1 revolution×1 minute60 seconds\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:

ω=157×2π60\omega = 157 \times \frac{2\pi}{60}

Now, let's calculate it.

ω=314π6016.44rad/s\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.

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Angular Velocity
Unit Conversion

Formulas

Angular Velocity (ω) = RPM × (2π radians/1 revolution) × (1 minute/60 seconds)

Theorems

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Suitable Grade Level

Grades 9-12