A toy cannon is placed at x0 (the initial position of cannonballs coming out of the cannon is x0 ) on a circular horizontal turntable of radius R, and is aimed at the center of the turntable . The turntable is spun up so that it is rotating at constant angular velocity Ω, and the cannon begins firing (with initial velocity horizontal) successive cannonballs toward the center of the turntable. Neglect the rotation of the Earth and air friction in working through this problem.
a) Describe the forces an observer on the turntable would measure on the cannonballs after they leave the cannon. (please include a diagram showing clearly the direction of the forces) Compare to the forces an observer who is not on the platform would measure (again, show clearly on a diagram the direction of the forces).
b) Determine the equation of motion of a cannonball, as observed in the frame of the turntable. Also solve this equation for the co-ordinates of the cannonball as a function of time.
c) Plot the solution (co-ordinates as a function of time) for the cannonball's motion given that R=5.0 m, Ω=0.5 rad/sec, and v0=1.0 m/s. Also sketch what the trajectory of the cannonball would look like if you were to make a bird's eye video of the cannonball motion by mounting a camera on the rotating turntable. Compare to the trajectory recorded by a video camera not mounted on the platform.