In the following problems, assume the following parameters: Mass of the bottom s

Question

In the following problems, assume the following parameters:

Mass of the bottom steel disc: 1.4678 kg

Mass of the upper steel disc: 1.4795 kg

Mass of the upper aluminum disc: 0.4614 kg

Radius of each disc: 63.3 mm

Radius of the take-up spool: r = 125 cm

Mass of the falling weight: 25 grams

1. Using the values given above, calculate the following: a) The moment of inertia of the lower, steel disc b) The moment of inertia of the upper, steel disc c) The moment of inertia of the upper, aluminum disc d) The combined moment of inertia of the two steel discs

Explanation / Answer

for a disc, moment of inertia, I = MR^2/2 where M is mass of disk and R is radius of disk a) M = 1.4678 kg , R = 63.3 mm = 0.0633 m I1 = 1.4678*(0.0633)^2 / 2 = 2.9407*10^-3 kg-m^2 b) M = 1.4795 kg , R = 63.3 mm = 0.0633 m I2 = 1.4795*(0.0633)^2 / 2 = 2.9641*10^-3 kg-m^2 c) M = 0.4614 kg , R = 63.3 mm = 0.0633 m I3 = 1.4678*(0.0633)^2 / 2 = 9.2439*10^-4 kg-m^2 d)combined moment of inertia of 2 disks would be sum of moment of inertia of 2 disks I = I1 + I2 = 5.9048*10^-3 kg-m^2

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