Two identical spheres, each of mass M and negligible radius, are fastened to opposite ends of a rod of negligible mass and length 2l. This system is initially at rest with the rod horizontal and is free to rotate about a frictionless, horizontal axis through the center of the rod and perpendicular to the plane of the page. A bug of mass 3M, lands gently on the sphere on the left. Assume that the size od the bug is small compared to the length of the rod. Express your answers to all parts of the question in terms of M, l, and physical constants.
a.) Determine the torque about the axis immediately after the bug lands on the sphere.
b.) Determine the angular acceleration of the rod-spheres-bug system immediately after the bugs lands.
At the instant that the rod is vertical (pointing up and down meaning it has rotated 90 degrees counterclockwise) determine each of the following:
c.) The angular speed of the bug.
d.) The angular momentum of the system
e.) The MAGNITUDE and DIRECTION of the force that must be exerted on the bug by the wphere to keep the bug from being thrown off the sphere.
T = r x F
T = Ialpha
L = r x p
L = Iw
The Attempt at a Solution
I realize this question has been asked on the forum before, but i have not found the other posts very helpful because they needed help with different parts
here are my solutions so far:
a) T = 3Mgl
b) alpha = 9g/16Ml
(solved by setting T = r x F = Ialpha)
c) w = sqrt(9(pi)g/16Ml)
(solved using w^2 = w^2 + 2alpha...)
d) L = 4Ml^2(sqrt(pi)g/Ml)
(solved by L = Iw)
e) I am stuck here! i dont know what concept to use!
Thanks in advance