The hour and minute hands of Big Ben in London are 2.66 m and 4.4 m long and hav
ID: 1460875 • Letter: T
Question
The hour and minute hands of Big Ben in London are 2.66 m and 4.4 m long and have masses of 69.2 kg and 107 kg respectively. Calculate the total angular momentum of the minute hand about the center point. Treat the hand as long, thin rod. Treat “into the clock” as the positive direction. Answer in units of kg · m2 /s.
Calculate the total angular momentum of the hour hand about the center point. Treat the hand as long, thin rod, and “into the clock” as the positive direction. Answer in units of kg · m2 /s.
Explanation / Answer
mh =69.2 kg, mm = 107 kg
Lh =2.66 m, Lm =4.4 m
Angular momentum L =Iw
Minute hand completes 60 min in 1revolution
w = 2pi/60min = (2*3.14)/3600 = 0.0017 rad/s
L =(ML2/3)w
L = (107*4.4*4.4/3)(0.0017)
Lm =1.174 kg.m2/s
Angular momentum L =Iw
Hour hand completes 12 hours in 1revolution
w = 2pi/12hr = (2*3.14)/(12*3600) = 1.45x10^-4 rad/s
L =(ML2/3)w
L = (69.2*2.66*2.66/3)(1.45x10-4)
Lh = 0.0709 kg.m2/s
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