Two thin rods are fastened to the inside of a circular ring. One rod of length D is vertical, and the other of length L makes an angle θ with the horizontal. The two rods and the ring lie in a vertical plane. Two small beads are free to slide without friction along the rods.
(a) Find an expression for the time interval required for the red bead to fall from the top of the ring to the bottom in terms of g and D.
(b) Find an expression for the time interval required for the blue bead to slide from the side of the ring to the bottom in terms of g, L, and θ.

Question

Two thin rods are fastened to the inside of a circular ring. One rod of length D is vertical, and the other of length L makes an angle θ with the horizontal. The two rods and the ring lie in a vertical plane. Two small beads are free to slide without friction along the rods.   
(a) Find an expression for the time interval required for the red bead to fall from the top of the ring to the bottom in terms of g and D. 
(b) Find an expression for the time interval required for the blue bead to slide from the side of the ring to the bottom in terms of g, L, and θ.

anonymous · Answer

The bead on rod with length D, will fall straight down. $$D = v_0 - {1 \over 2} g t^2$$

The bead on rod with length L, will fall at an angle. Gravity must be broken up to find the component that acts along the rod of length L. $$L = v_0 - {1 \over 2} g \sin(\theta) t^2$$

anonymous · Answer

Thanks for the help I appreciate it