A uniform disk is constrained to rotate about an axis passing through its center and perpendicular to the plane of the disk. If the disk starts with an angular velocity of 3.0 rad/s and is subject to a constant angular acceleration of 9.0 rad/s2, find the angular displacement of a point on the rim of the disk as it rotates under these conditions for 18 s. (Assume the positive direction is in the initial direction of the rotation of the disk. Indicate the direction with the sign of your answer.)

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?