Sally the physics student conducts the following experiment: There is a popular playground ride which is just a horizontal wooden disk free to rotate around a vertical axis. Sally hops onto the disk (spinning counter clock wise with angular velocity [tex]\omega[/tex] ) with a bunch of tennis balls. With practice, Sally discovers that she can throw a tennis ball such that the path of the ball passes through the axis and returns to her.
Throughout this problem neglect air resistance and neglect the vertical component of the ball's velocity (ie pretend the ball's path is limited to a horizontal plane). You may also neglect any effects due to the rotation of the earth.
A. Sketch a path of the ball r (t) in earth frame. Choose the coordinate system to coincide with axis of ride.
(I think this is just a straight chord)
B. Find an expression for r(t) in earth frame. Give an answer in terms of Sally's distance from the axis R and speed of the ball v. (Hint check that v(t) is constant)
(I got just r(t) = R + vt) Too simple?
C. Find the speed of the ball v in terms of R and [tex]\omega[/tex] assuming that the ball passes through the axis and returns to Sally.
D. Transform the coordinates to find x'(t) and y'(t), the path of the ball in the rotating frame centered on the axis and co-spinning with the ride. Sketch the path of the ball in the rotating frame.
(need the prior answer)
E. Take the time derivative of r'(t) to find the components of the ball's velocity in the rotating frame. Check that v(t)=v'(t) + [tex]\omega[/tex] x r' (t).
(need prior answer)
a = a' + (omegadot) x r' + 2(omega) x v' + (omega) x (omega x r')
v = v' + (omega) x r' + v0