18.A stroboscope is to be used to measure the rotational speed of a shaft. On th

Question

18.A stroboscope is to be used to measure the rotational speed of a shaft. On this shaft a series of eight equally-spaced spots have been painted around the periphery.

a)Determine an expression for the possible shaft speeds, s, in revolutions per minute as a function of the strobe frequency f measured in Hertz.

If the strobe frequency is slightly higher than eight times the shaft rotation speed will the apparent rotation be in the same or the reverse direction of the true rotation direction of the shaft?

Explanation / Answer

Hertz is 1/second and RPM would be 1/minute

hertz * 60 = RPM
RPM / 60 = hertz

To avoid confusion, periodically varying angles are typically not expressed in hertz, but rather in an appropriate angular unit such as radians per second. A disc rotating at 60 revolutions per minute (RPM) can thus be said to be rotating at ?6.283 rad/s or 1 Hz, where the latter reflects the number of complete revolutions per second. The conversion between a frequency f measured in hertz and an angular frequency ? measured in radians/s are:

? = 2?f and f = ?/(2?)

If you are measuring as Hertz how many cycles of the motor shaft per second is fine the convertion mentioned down

1 Hz = 60 RPM

But if you are talking about Electrical Hz, you need the data of your motor. For example a motor that in the template shows 1800 rpm @ 60 Hz, means that with an electrical signal of 60 Hz will turn at 1800 RPM. Then the convertion will be:

60 Hz = 1800 RPM
1 Hz = 30 RPM

And those values are the ones that an inverter or drive uses for control the motor speed.

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