Question

You're staring at a traditional clock for 1 hour. after 1 hour, what is the angular displacement of the second hand? the minute hand? the hour hand?

Answer 1

During the hour, the second hand will have traveled a full 360 degrees times 60 for a total displacement of 21600 degrees or 21600*pi/180 = 120 pi radians, or approximately 376.99 radians. Also during that hour, the minute hand will have gone around a full 360 degrees, or 360*pi/180 = 2 pi radians, or approximately 6.28 radians. And finally, the hour hand will have gone 360/12 = 30 degrees or 30*pi/180 = pi/6 radians, or approximately 0.52 radians.