Maximum angular velocity of a DC motor powered by a charged capacitor

[Jumponright]

Homework Statement

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.

Homework Equations

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

 

[Hesch]

Is it possible to equate the energy of a capacitor and the kinetic energy of the motor like this?

12CV2=12Iɷ2​

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 ?

 

[Jumponright]

not really, can you explain it? thanks

 

[Hesch]

can you explain it?

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, Z_C(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.

 

[Jumponright]

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

 

[Hesch]

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.

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.