Athin rod of length l and mass m rotates around an axis that passes through a point one-third of the way from the left end.1) which of the following will decrease the rotational kinetic energy of the rod by the greatest amount? a) decreasing the mass of the rod by one fourth, while maintaining its length. b) decreasing the length of the rod by one half, while maintaining its mass. c) decreasing the angular speed of the bar by one half. d) each of the above scenarios will decrease the rotational kinetic energy by the same amount.

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?