Here we will be examining the motion of a frictionless puck that we are sliding across a merry-go-round. The merry-go-round has a radius of 2 meters, a rotational period of 8 seconds, and is spinning counterclockwise.
Part A
You would like to start the puck with a velocity that will take it directly across the center of the merry-go-round so that you catch it on the other side. In other words, you'd like yourself and the puck to arrive at the opposite side at the same time.
Determine the needed speed of the puck as seen in the inertial reference frame.
Determine the needed speed and angle of the puck's initial velocity as seen in your rotating reference frame.
Will you need to shoot the puck at some angle to the left or right of straight across the merry-go-round?
Part B
There are no other forces acting on the puck as it makes its way across the merry-go-round, so you just need to worry about the Coriolis and centrifugal forces. Numerically solve for the motion of the puck and plot it. Does it make sense? What is the greatest distance the puck ever gets from you?
Part C
Frequently when considering these types of rotating reference frame problems, I find it useful to have a comparison of both the motion as seen in the inertial reference frame and the motion as seen in the rotating reference frame. Create an animation of the puck's motion across the merry-go-round, with a subplot on the left depicting the motion as seen in the stationary frame and the subplot on the right showing the motion as seen in the rotating reference frame (you can use your same data as in Part B). Draw the circle of the merry-go-round on both plots, and on the inertial reference frame plot, also include a point that shows your position on the edge of the merry-go-round as you go around (so that we can see both the puck and you arrive at the opposite side at the same time). Make sure to label and title your plots!