By relative velocity, we mean velocity with respect to a specified coordinate system. (The term velocity, alone, is understood to be relative to the observer’s coordinate system.)
(a) A point is observed to have velocity Va relative to coordinate system A.What is its velocity relative to coordinate system B, which is displaced from system A by distance R? (R can change in time.)
(b) Particles a and b move in opposite directions around a circle with angular speed ω, as shown. At t = 0 they are both at the point r = lˆj, where l is the radius of the circle. Find the velocity of a relative to b.
(c) Sketch the motion of the particle.
The Attempt at a Solution
I was able to solve part A and found Va=Vb + dR/dt. I'm pretty confident in this answer.
I was also able to solve part B. I found dR/dt to be 2wlcos(wt). I then plugged this into the answer from part A and got Va=Vb + 2wlcos(wt). I'm pretty confident in this answer as well.
My issue is with part C. To graph the position, I integrated the answer from part B and got Rx=Vbt+2lsin(wt). I believe I did this right, but if you graph it the sin function does not go linearly across the graph as it normally does, but instead gradually increases due to the Vbt term in front of it. This does not seem to make sense in the real world because the particles are going around a circle so they should not be gradually getting farther apart over time? I'm pretty stumped on this. Any input about this would be appreciated.
Thanks for all the help!