# Electric motor(calc. angular velocity

1. Jun 8, 2013

### antoman

First of all im sorry for my awful english.

1. The problem statement, all variables and given/known data
Electric motor starts turning wheel with a constant power of P=25W and J=3 kg*m^2. With what angular velocity the wheel spins after 7s(from start), if the efficiency is 60%

2. Relevant equations
P=M*ω
M=J*α

3. The attempt at a solution

Ok so i have equasion that gives correct number(solution) for this particular case, but i wanna to know how did guy that wrote it came up with it and if its correct anyway.
so, equasion is:

I tried to get to this equasion by myself so i did this:
ω=P/M=P/(J*α)=P*t/(J*ω) so
ω^2=P*t/J
ω=sqrt(P*t/J)

The other thing that bothers me is that efficiency is not iven used. So any help how to develop correct equasion would be nice.

2. Jun 8, 2013

### voko

Power times time is total energy. Efficiency tells you how much of the total energy becomes the kinetic energy of the rotating wheel.

3. Jun 8, 2013

### TSny

The above method uses energy concepts. If you recall the formula for the rotational KE of an object, you should be able to see where the formula comes from.

To me, the statement of the problem is not very clear on whether the given power is the power of the motor or the power delivered to the wheel. Apparently, it's the power of the motor. So, as voko pointed out, you need to take the efficiency into account to get the power delivered to the wheel.

Here you are using P = Mω where P is the power delivered to the wheel and M is the instantaneous torque (moment). This equation holds at each instant of time. You are given that P is constant and you know that ω is not constant. So, is M constant or not? If not, then you can't use constant acceleration equations such as ω = αt.

Last edited: Jun 8, 2013
4. Jun 8, 2013

### antoman

Problem is i dont know if M is constant, but guessing from what you wrote its not, so my equations are all wrong.

So... Wrot=2*ω^(2)/J
ω^2=Wrot*2/J

edited: A=Wk2-Wk1 --> A=Wrot

Thanks :)

Last edited: Jun 8, 2013
5. Jun 8, 2013

### TSny

No need to guess. Use logic. If P = Mω and you know that P is constant while ω is not constant, then you can deduce whether or not M is constant.

It will help a lot if whenever you use a symbol, you state what the symbol represents. What do the symbols Wrot, Wk2, Wk1, and A stand for?

6. Jun 8, 2013

### antoman

Wrot...KE
Wk1.. KE at t=0
Wk2...KE when t=7
A.. work

Last edited: Jun 8, 2013
7. Jun 8, 2013

### TSny

Are you sure you are using the correct formula for rotational kinetic energy?

[EDIT]
Ok, this looks correct.