Rotation of a Clock

A clock is a very helpful invention and there is plenty of physics behind it. Today I am going to analyze he rotational motion behind a clock. 

First off, when any hand completes one revelution, whether it means a minute, an hour, or 12 hours, the angular displacement is 2(pi) radians or 360°. This of course allows us to find the angular velocity (w). If we are talking about an ideal clock that rotates at a constant rate, we can determine that the second hand travels pi/30 rad/s. Next, the minute hand travels pi/1800 rad/s. Lastly, the hour hand travels pi/108000 rad/s. The angular velocity will be the same on every clock, but the linear speed of the outermost part will be greater the larger the clock. 

Now this gets a little more complicated if we have a clock that ticks (which a lot do). The second hand does not travel at a constant velocity, rather it accelerates then decelerates, every time it travels one notch (pi/30) rad. On a certain watch I have, it takes about .3s for the hand to move one tick, meaning he acceleration and deceleration are about 9.3 and -9.3 rad/s/s. Clearly clocks are very complex but have some cool physics.