Physics at Case

My job on Campus is at the library as a Library Automated Storage and Retrieval (LASR) assistant. LASR is a system used to retrieve stored books using a robot like the one below. 

(https://www.google.com/search?q=library+automated+storage+and+retrieval+system&espv=2&biw=1452&bih=878&tbm=isch&source=lnms&sa=X&ved=0ahUKEwiy2KPn5o3QAhUo_IMKHRuIAzkQ_AUIBigB#imgrc=fEK_KxnjcA-rhM%3A)

These robots can carry a maximum load of 500 pounds (227 kg). Colgate has 4,272 steel storage bins (4 ft by 2 ft with varying heights) stored in LASR at Case Geyer library. The robot operates using two tracks operated by four gears each which rotate to "grab" the bins using pegs that fit into handles on the edge of each bin. 

(http://continuum.utah.edu/wp-content/uploads/2014/11/201301011_UULIBRARYFEATURE_0194-620x413.jpg)

While working on Tuesday I measured (roughly) the size of the gears used to rotate the track. The diameter of each gear is roughly 4.5 inches (.1143 meters) making the radius .05715 meters. Since I couldn't get too close to the machine while it was operating, I did my best to measure how long it took for the track to make half a rotation in order to grab the bin (4 seconds). This means that the track travels 1.2192 meters in 4 seconds, giving it a velocity of .305 m/s. 

If we say the gears have the same speed as the track then the angular velocity of the gears can be measured by v/r = (.305 m/s) / (.05715 m) = 5.34 radians/second.

If the gears start at an angular velocity of zero and end at an angular velocity of 5.34 r/s over the course of 4 seconds, then the angular acceleration is 1.335 r/s^2.