Understanding Angular Velocity
Angular velocity is a measure of how quickly an object rotates around a point or axis. It is usually expressed in radians per second (rad/s).
Given Data
- The particle rotates 100 times per minute.
Conversion to Radians
- One complete rotation (360 degrees) is equivalent to 2π radians.
- Therefore, for 100 rotations:
- Total radians = 100 rotations × 2π radians/rotation = 200π radians.
Time Conversion
- Since we need angular velocity in rad/s, we must convert minutes to seconds:
- 1 minute = 60 seconds.
- Thus, 100 rotations per minute is:
- Time = 60 seconds.
Calculating Angular Velocity
- Angular velocity (ω) can be calculated using the formula:
- ω = Total radians / Time in seconds.
- Substituting the values we have:
- ω = 200π radians / 60 seconds.
Final Result
- Simplifying gives:
- ω = (200π / 60) rad/s = 10π/3 rad/s.
- This value is approximately 10.47 rad/s when calculated numerically.
Summary
- The angular velocity of a particle rotating at 100 times per minute is approximately 10.47 rad/s.
- This value reflects the rapid circular motion and is important for understanding dynamics in rotational systems.