induction motor and capacitance

HI all. I am new to CE.

consider this situation:

we have an induction motor in hand , which is of capacitor-start-capacitor-run type. the datasheet of the motor says that its maximum speed is 380 rpm.

the motor has a 2 microfarad capacitor fitted external to its body.

it now becomes evident that the 2 mf capacitor enables the motor to run at 380 rpm.

now how do we determine the speed of the motor if its capacitor was replaced with that of a different capacitance value.

we do not have any tachometers in hand to measure the spindle speed physically. so how do we determine the speed mathematically ?

my approach is as follows : for example if the 2 mf cap was replaced with a 1 mf cap, then the speed will vary proportionally, that is it will be reduced by half to 190 rpm.

is this calculation correct ? does the speed vary with capacitance linearly ?

Pawl supiran

is this calculation correct ? does the speed vary with capacitance linearly ?

That is not the purpose of the capacitor. The run capacitor ensures a proper rotating magnetic field is maintained. It has to be sized for each capacity of motor and the winding. Changing the value will drastically affect performance.
The speed cannot be controlled by varying the running capacitance.
Motor capacitor - Wikipedia