# Angular velocity of a motor

1. Sep 12, 2015

### Jumponright

1. The problem statement, all variables and given/known data
Hi all I am doing a school physics project and I am trying to find the maximum angular velocity of a DC motor. I have built a circuit consisting of a charged capacitor (of known voltage) and a motor. I then try to predict the maximum angular velocity attained by the motor.

2. Relevant equations

3. The attempt at a solution
Is it possible to equate the energy of a capacitor and the kinetic energy of the motor like this?
$$\frac{1}{2} C V^2=\frac{1}{2}Iɷ^2$$
can i similarly integrate it to find the angular displacement?

Thanks for the help guys

2. Sep 12, 2015

### Hesch

No, you cannot, because there will be conductive losses in the windings of the motor, and the capacitor will not be completely discharged ( due to the back-emf of the motor ).

You must make a complete model of the capacitor/motor, including:

- Capacitor voltage (t).
- Back emf in the motor.
- Self induction in the motor.
- Motor inertia.
- Resistance in motor windings.

The easiest way is to do this by Laplace transforms.

You know how to do that ?

3. Sep 12, 2015

### Jumponright

not really, can you explain it? thanks

4. Sep 12, 2015

### Hesch

Well, I can explain it ( with some diagrams, and so on ).

But are you familiar with Laplace transforms at all ?

For example: The impedance of a capacitor, ZC(s) = 1/(sC) ?
Or when you ( in time-domain ) integrate a signal, you divide by s in the Laplace domain ?

If you are familiar with that, I can sketch a diagram with an explanation.

5. Sep 15, 2015

### Jumponright

I have just read a bit on Laplace transforms, I can try to understand it

6. Sep 16, 2015

### Hesch

Do you have some (realistic) values as for the above? ( also the value of the capacitor ).

I think that an algebraic explanation will be a mess.