1. Consider a clock with hour, minute, and second hands. For each hand. period,
ID: 1796564 • Letter: 1
Question
1. Consider a clock with hour, minute, and second hands. For each hand. period, the frequency, and the angular frequency2 (Hint: For the period, find the time for the hand to make I revolution in seconds). Please calculate the frequencies here to 3 what is the significant figures. 2. In the simple pendulum discussion above, we claimed that "if is small, cos-1 and a,-0." To 3 significant figures, what angle would make about a 2% error in the assumption cos 1? (use your calculator) At this angle, how does ay compare with a? (Hint: at 2% error, we can still assume the magnitude of FT-mg. Substitute mg for Fr in the equations you derive for a and ay to obtain numerical values.)Explanation / Answer
for hour hand
period is T = 12 hours = 12*60*60 = 43200 sec
frequency is f = 1/T = 1/43200 = 2.31*10^-5 Hz
angular frequency is w = 2*pi*f = 2*3.142*2.31*10^-5 = 1.45*10^-4 rad/s
for minute hand
T = 60 min = 60*60 = 3600 sec
f = 1/T = 1/3600 = 2.78*10^-4 Hz
w = 2*pi*f = 2*3.142*2.78*10^-4 = 0.00175 rad/s
for seconds hand
T = 60 sec
f = 1/T = 1/60 =0.0167 Hz
w = 2*pi*f = 2*3.142*0.0167 = 0.105 rad/s
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