 #1
 49
 12
 Homework Statement:
 Find the number of revolutions by the cylinder.
 Relevant Equations:

$$ \tau = I \alpha $$
Change in Kinetic energy = Work done
Hello, I'm stuck in this rotational motion problem (advanced high school level).
Source: Problems in General Physics IE Irodov
My attempt(s):
First I tried using work done by the moment of friction (mgkR) and equated it with change in KE.
I got the answer as ## \frac{R (\omega_0)^2}{8 \pi g k} ##.
However, the correct answer is ## \frac{(1+k^2)R (\omega_0)^2}{8 \pi g k(1+k)} ## .
The first mistake I thought of is not including centripetal, but the centripetal is varying with ## \omega ## and whenever I solve it that way I am not even getting close to the answer. Using ## \tau=I \alpha ## is getting nowhere either.
Any hint is appreciated. Thank you.
Source: Problems in General Physics IE Irodov
My attempt(s):
First I tried using work done by the moment of friction (mgkR) and equated it with change in KE.
I got the answer as ## \frac{R (\omega_0)^2}{8 \pi g k} ##.
However, the correct answer is ## \frac{(1+k^2)R (\omega_0)^2}{8 \pi g k(1+k)} ## .
The first mistake I thought of is not including centripetal, but the centripetal is varying with ## \omega ## and whenever I solve it that way I am not even getting close to the answer. Using ## \tau=I \alpha ## is getting nowhere either.
Any hint is appreciated. Thank you.