can someone help me with this problem? In an angular momentum experiment we drop
ID: 1484474 • Letter: C
Question
can someone help me with this problem?
In an angular momentum experiment we drop a disc of mass 230 g and radius 2.22 cm onto a rotating disc of equal mass and radius. We measure the initial and final angular velocity, taking five values of omega before and after the drop. Find the average angular velocity in both trials. Find the standard deviation for initial angular velocity only. Show your work (sample calculation) for the standard deviation calculation. Assume a 5% uncertainty in mass and 1% uncertainty in radius. Find the initial angular momentum and its uncertainty. Find the final angular momentum (without uncertainty). How many sigmas is your final angular momentum from your initial angular momentum? (Take into account only the uncertainty of initial angular momentum.)Explanation / Answer
To find the average, we just need to sum up all the angular velocity values and just divide it with the total number of velocity
So,average of the initial angular velocity is,
wia=2.09+2.16+2.23+1.98+2.02/5=2.096rad/sec
average of final angular vleocity is,
wfa=1.12+0.98+1.07+1.01+0.92/5=1.02 rad/sec
we need to find w-wia for each values
(2.096-2.09)2=0.000036
(2.096-2.16)2=0.004096
(2.096-2.23)2=0.0179
(2.096-1.98)2=0.0134
(2.096-2.02)2=0.0049
take the sum of all the values
standard deviation=sqrt(sum(w-wia)2/n-1)=sqrt(0.0411/4)=0.1014
For final velocity,
(1.02-1.12)2=0.0009
(1.02-0.98)2=0.0016
(1.02-1.07)2=0.0025
(1.02-1.01)2=0.0001
(1.02-0.92)2=0.01
standard deviation=sqrt(sum(w-wfa)2/n-1)=sqrt(0.0151/4)=0.0614
b) we know that angular velocity,w=v/r
Momentom,p=mv or v=p/m
So w=p/mr
So the uncertanity will be,1/5% for both the initial and the final
c)Number of sigmas that can make final angular momentom is from the initial sigma is,1.02/0.1014=10.05
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.