Rotations per minute to radians per second conversion: 2500 RPM to rad/s unit analysis.
RPM to rad/s conversion: we convert a given angular velocity in RPM (rotations per minute) to radians per second using a series of conversion factors. The radians per second conversion requires applying two conversion factors to cancel the units of rotations and minutes in favor of radians and seconds.
First, we get a reminder that an entire circle covers an angle of 2pi radians. This gives us the conversion 1 rotation = 2pi radians. We can turn this into the conversion factor (a factor of 1): 2pi radians/1 rotation =1. We multiply 2500 rotations/minute * 2pi radians/rotation, the units of rotations cancel out, and we are left with radians per minute.
Next we use the fact that 1 min =60s. This gives us a conversion factor of 1min/60s =1. We multiply by the conversion factor to get 2500 rotations/minute * 2pi radians/rotation*1min/60s, and we are left with units of radians per second.
Now we multiply all the numerators and divide by the product of all the denominators, and we're done converting 2500 RPM to rad/s!