Use the Biot-Savart law to fi nd the magnetic fi eld inthe frame of an electron circling a nucleus of chargeZe. If the velocity of the electron around the nucleusis v and the position vector of the proton with respectto the electron is r, show that the magnetic fi eld at theelectron isB Ze4pP0Lmc 2r 3 where m is the electron mass and L is the angularmomentum, L mr v.

CHAPTER ８８ Rotation Circular Motion ● Circular Motion is characterized by two kinds of speeds: ○ Tangential (or linear) speed ○ Rotational (or circular) speed ● Tangential Speed ○ The distance traveled by a point on the rotating object divided by the time taken to travel that distance is called its tangential speed (symbol v) ○ Points closer to the circumference have a higher tangential speed than points closer to the center ○ m/s ● Rotational Speed ○ Rotational (angular) speed is the number of rotations or revolutions per unit of time (symbol omega) ○ All parts of a rigid merry go round or turntable turn about the axis of rotation in the same amount of time ○ SO all parts have the same rotational speed ○ RPM ● Rotational Inertia ○ Depends upon ■ Mass of object ■ Distribution of mass around axis of rotation ○ The greater the rotational inertia, the harder it is to change its rotational state ● Torque ○ The tendency of a force to cause rotation is called torque ○ Torque depends upon three factors ■ Magnitude of the force ■ The direction in which it acts ■ The point at which it is applied on the object ○ T = rf ■ R is the lever arm, depends on where the force is applied and what direction it acts