I need help with my finals, if anyone can help me it will be great.

Two masses are connected by a rope that hangs over a pulley as shown below. the pulley is a uniform cylinder of radius 푅=0.381meters and mass 푀=3.1푘푔. initially 푚"is on the ground and 푚#rests 2.5 meters above the ground. if the system is released, use conservation of energy to determine the speed of 푚#just before it strikes the ground. assume the pulley bearing is frictionless.

Cyclotrons are widely used in nuclear medicine for producing short-lived radioactive isotopes. these cyclotrons typically accelerate h- (the hydride ion, which has one proton and two electrons) to an energy of 5 mev to 20 mev. this ion has a mass very close to that of a proton because the electron mass is negligible—about 1 2000 of the proton’s mass. a typical magnetic field in such cyclotrons is 1.9 t. (a) what is the speed of a 5.0-mev h-? (b) if the h- has energy 5.0 mev and b = 1.9 t, what is the radius of this ion’s circular orbit?

What is the moment of inertia i of this assembly about the axis through which it is pivoted? express the moment of inertia in terms of mr