Answer
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Step 1:: Understand the problem
To convert rotations per minute (RPM) to radians per second (rad/s), we need to use a conversion factor that relates the two units. The conversion factor is derived from the definition of radians and the relationship between the circumference of a circle and its radius.
Step 2:: Find the conversion factor
- $60\; s$ is the time taken for one full rotation in seconds when the angular velocity is in RPM
The conversion factor from RPM to rad/s can be found using the following formula: Where:
Step 3:: Apply the conversion factor
To convert a given angular velocity in RPM to rad/s, simply multiply the angular velocity in RPM by the conversion factor:
Step 4:: Simplify the equation
We can simplify the equation by canceling out the units:
Step 5:: Calculate the result
To calculate the angular velocity in rad/s, multiply the angular velocity in RPM by the simplified conversion factor:
Final Answer
To convert RPM to rad/s, multiply the angular velocity in RPM by the conversion factor $\frac{\pi}{30}$.
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