I'm getting crazy with this problem and I think that it's pretty simple.
An helicopter's helix is spinning at initial speed $w_0=200\ rpm$, all of a sudden the motor stops and it decreases its velocity with a not constant acceleration of $\alpha=-0,01\cdot w \frac{rad}{s^2} $.
The question is: how many revolutions will it make until it stops?
I know that it can't be solved using regular kinematics formulas because the acceleration is not constant so I tried with the next chain rule:
$$a(x) = \frac{dv}{dt} = \frac{dv}{dx}\frac{dx}{dt} = \frac{dv}{dx}v$$
that I've seen in another question where the acceleration depended on the $x$, and you can solve the problem with $a(x)dx = vdv$ but in my case it depends on the velocity $w$ and I don't know what to do!
I'm trying to get something like $a(w)dw= ... $ but I don't know how to arrive. This is my closest attempt:
$$\alpha=\frac{dw}{dt}\cdot\frac{dw}{dw}\rightarrow \alpha dw=\phi dw$$
and here I'm stucked.
I will appreciate any help! Thank you!
