# Acceleration time of unloaded motor

I want to use a motor to generate musical tones by spinning a disk. The disk will have optically printed sound waves on it.

I would like to know how fast the motor will be able to change speed from one note to another.

The motor will be driven by 3 phase variable frequency drive.

So for example how fast will it be able to double its rpm from 100 to 200 if I instantaneously double the drive frequency?

We can ignore the inertia of the disk for now because I don't know it yet. It would be good to just know a general way to solve this problem, then I calculate for a different inertia.

The motor I am thinking of using is 3 phase brushless slotless type

From the data sheet

Nominal torque (max. continuous torque) 94.6 mNm

Nominal voltage 24v

Nominal current (Max continuous current) 7.58A Stall torque 3220 mNm

Rotor inertia 33.3 gcm²

Torque constant 13.6 mNm/A

Speed constant 700 rpm/V

Mechanical time constant 1.82 ms

$$M=J\alpha$$
$$\alpha=\frac{M}{J} = \frac{0.0946}{3.36*10^{-6}}\approx 28000\;rad/s^2$$ $$dt=\frac{d\omega}{\alpha}= \frac{100*2\pi}{60*28000} \approx 0.4ms$$