Chapter 9, Problem 67P

Two particles of masses $m_1$ and $m_2$ move uniformly in different circles of radii $R_1$ and $R_1$ about the origin in the x, y-plane. The coordinates of the two particles in meters are given as follows ( $z=0$ for both). Here t is in seconds:

   $x_1\left(t\right)=4\cos \left(2t\right)$

   $y_1\left(t\right)=4\sin \left(2t\right)$

   $x_2\left(t\right)=2\cos \left(3t-\frac{\pi }{2}\right)$

   $y_2\left(t\right)=2\sin \left(3t-\frac{\pi }{2}\right)$

a. Find the radii of the circles of motion of both particles.

b. Find the x- and y-coordinates of the center of mass.

c. Decide if the center of mass moves in a circle by plotting its trajectory.