In an angular momentum experiment we drop a disc of mass 230 g and radius 2.22 c

Question

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. 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

MI of single disk  I1 = 0.23*(2.23x10^-2)^2/2 = 0.567x10^-4

uncertainity = 5+1+1 = 7%

Average angular speed = 2.1 SD = 0.091

       uncertainity = 0.091/2.1*100 = 4.3 %

anglar momentum = Iw = 0.567x10^-4*2.1 =1.191x10^-4

                       uncertainity = 7+4.3 = 11.3 %

SD of L = 0.135x10^-4

final MI = 0.567x10^-4*2 = 1.34x10^-4

average final angular speed = 1.02

final angular momnetum = 1.34x1.02 = 1.367x10^-4

b)

sigma or SD of initial L = 1.191x10^-4x0.117 = 0.135x10^-4

final L = 1.367x10^-4 is 10 sigmas from inital angular momentum

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