What is the calculation for determining motor shaft RPM using a tachometer?

[Tweaked9107]

I am trying to figure out the speed that a motor shaft is running at but i have no reference materials to work with. I had to place a tachometer on the outside of the shaft as there was no centre drilled hole to work from. I got the following results:

Diameter of tachometer: 31.5mm
Diameter of motor shaft: 12mm
RPM of tachometer: 1400rpm

What calculation would i need to work out the rpm of the motor shaft?

 

[cragar]

wouldn't the rpm of the shaft be 1400 rpm unless I am missing something , or are you wanting the angular velocity

 

[Filip Larsen]

If the tachometer is of the type that uses a contact wheel to pick up rotation, then the shaft RMP_s = RPM_t * d_t/d_s, where subscript s is for shaft and t for tachometer. With the values you gave, the 1400 tachometer RPM then corresponds to 3675 shaft RPM.

 

[Tweaked9107]

If the tachometer is of the type that uses a contact wheel to pick up rotation, then the shaft RMP_s = RPM_t * d_t/d_s, where subscript s is for shaft and t for tachometer. With the values you gave, the 1400 tachometer RPM then corresponds to 3675 shaft RPM.

Yeh that's the answer I had as well. I just thought it seemed too simple to be the same principle as gear ratio's. Thanks for your help.