A bicycle racer is going downhill at 13.0 m/s when, to his horror, one of his 2.03 kg wheels comes off when he is at top of the hill. We can model the wheel as a thin-walled cylinder of diameter 0.85 m, with a moment of inertia of 0.367 kg-m2. (Neglect the small mass of the spokes). Consider its motion is rolling without slipping, and downhill angular acceleration of 2.3 rad/s2. What distance has the wheel traveled, in meters, when it is going at 43.3 m/s?

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?