- #1
Cosmophile
- 111
- 2
Moved from a technical forum, so homework template missing.
Hey, all. I've decided to go back and work on some old K&K problems that I didn't finish last time. Here's a neat one that's been giving me trouble.
I hadn't attempted problem a yet (I admittedly completely overlooked it by accident!). For b, I had a difficult time finding a good starting point. I initially took ##B##'s frame of reference to be stationary and decided that would mean ##A## would be the only object moving.
For this case, I centered the circle at the origin ##(0,0)##. Let ##A## and ##B## be two points on the circle. From ##B##'s frame, ##A## travels around the circle. ##A##'s position is given by the vector ##\vec{R}##, drawn from ##B##. ##\vec{R}## is a chord on the circle. ##\theta## is the angle made by ##\vec{R}## and the line ##BO = L = AO##, where ##O## is the origin ##(0,0)##.
Because I am finding the velocity of ##A## from ##B##'s point of view, the velocity vector will not be purely tangential to the circle. So, in polar coordinates, I get:
[tex] \vec{v_A} = -v \sin(\theta) \hat{r} + v \cos(\theta) \hat{\theta} [/tex]
After discussing this with a friend who has completed his undergrad, he informed me that I was wrong. From ##B##'s point of view, both ##A## AND the circle are moving. If this is the case, I am having a difficult time finding a starting point. So, help is welcome as always!
I hadn't attempted problem a yet (I admittedly completely overlooked it by accident!). For b, I had a difficult time finding a good starting point. I initially took ##B##'s frame of reference to be stationary and decided that would mean ##A## would be the only object moving.
For this case, I centered the circle at the origin ##(0,0)##. Let ##A## and ##B## be two points on the circle. From ##B##'s frame, ##A## travels around the circle. ##A##'s position is given by the vector ##\vec{R}##, drawn from ##B##. ##\vec{R}## is a chord on the circle. ##\theta## is the angle made by ##\vec{R}## and the line ##BO = L = AO##, where ##O## is the origin ##(0,0)##.
Because I am finding the velocity of ##A## from ##B##'s point of view, the velocity vector will not be purely tangential to the circle. So, in polar coordinates, I get:
[tex] \vec{v_A} = -v \sin(\theta) \hat{r} + v \cos(\theta) \hat{\theta} [/tex]
After discussing this with a friend who has completed his undergrad, he informed me that I was wrong. From ##B##'s point of view, both ##A## AND the circle are moving. If this is the case, I am having a difficult time finding a starting point. So, help is welcome as always!