Recent content by cantleave

I'm having an exam in 2 days, after that I will be able to concentrate more on this problem. Please don't close the thread. I'll be back as soon as I can. Thank you

Thanks for reopenning the thread. There was no problem statement thus there was no mentioning of friction, neither that it should be ignored nor that it should be taken into consideration. The professor gave me the figure, listed the parameters that are known (by "known" I mean they could be...

\dot{r} = r\hat{r}' = r\dot{Θ}\hat{Θ} \ddot{r}= r(\dot{Θ}\hat{Θ})' = r(\ddot{\theta}\hat{\theta}-\dot{\theta}^{2}\hat{r}) Could you tell me please in a few words what are we trying to achieve? I mean, what is our strategy?

Ok. I think got it now. r doesn't depend on Θ. r is a constant

The distance traveled by the object on the path is the full length of the circle divided by the angle θ. As the object moves, θ becomes greater thus the formula r = 2piR/θ (I forgot the R, the radius of the circle) By distance did you mean the shortest way to the object from the origin which is...

I thought r was the position vector that starts from the center of the circle. r = 2pi/θ? or my other guess would be the integral of velocity?

$$ \dot{r} $$ is the first derivative of the position function with respect to time = velocity, and $$ \ddot{r} $$ is the second derivative of the position = acceleration. I suppose the thetas and funky stuff comes from the fact that we convert from Cartesian to polar coordinates. I'm familiar...

a = (r'' - rΘ'^{2})\hat{r} + (2r'Θ' + rΘ'')\hat{Θ}

I understand. What about part 2,3 and 4? How do I proceed further?

I wasn't given exact values, it was just stated that those are known parameters, could be any number.

Yes, it does move counterclockwise. So what do we do next?

If there is no friction $$ \vec{F} = (mgcosθ-N)\hat{r} - mgsinθ\hat{θ} $$ Or is this what you were referring to? I can't get this latex work

Yes, this does make sense! Thank you. I suppose though it get's more complicated. But wait a minute, did I put the friction force in the right sense? Shouldn't it be pointing toward the opposite direction of the tendency of movement? Or do we assume that the object moves only counterclockwise?

Mgsinθ is along the tangential direction.

Yeah, right, I need to consider the projections of M on the radial and tangential directions. Mcos(\frac{pi}{2}-Θ) + Mcos(Θ) = M But how do these relate to T and N?