TWO IDENTICAL SPHERE, 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, AS SHOWN, AND IS FREE TO RAOTATE ABOUT A FRICTIONLESS, HORIZONTAL AXIS THROUGH THE CENER TO THE ROD AND PERPENDUICULAR TO THE PLANE OF THE PAGE. AN INSECT, OF MASS 3M, LANDS GENTLY ON THE SPHERE ON THE LEFT. ASSUME THAT THE SIZE OF THE INSECT 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 INSECT LANDS ON THE SPHERE.

B) DETERMINE THE ANGLULAR ACCELERATION OF THE ROD-SPHERE-INSECT SYSTEM IMMEDIATELY AFTER THE INSECT LANDS.

THE ROD-SPHERE-INSECT SYSTEMS WSING ABOUT THE AXIS. AT THE INSTANT THAT THE ROD IS VERTICAL, DETERMINE EACH OF THE FOLLOWING:

C) THE ANGULAR SPEED OF THE INSECT.

D) THE ANGULAR MOMENTUM OF THE SYSTEM

E) THE MAGNITUDE AND DIRECTION OF THE FORCE THAT MUST BE EXERTED ON THE BUG BY THE SPHERE TO KEEP THE BUG FROM BEING THROWN OFF THE SPHERE.