Two discs are fastened together, so they act as one object with a common axis of

Question

Two discs are fastened together, so they act as one object with a common axis of rotation. R_1 = 3 m, and R_2 = 4.5 m. Each disc is 10 cm thick and is constructed of a material with a density of 20kg/m^3. Two masses hang from thin cables, as shown. a) Calculate the moment of inertia of the composite disc. b) If M_1 = 66 kg, what is M_2 such that no angular acceleration results in the system? c) If 33 kg is added to M_1, and M_2 is the same as part b) calculate the angular acceleration of the discs, the linear accelerations of both masses and the tensions in both cables.

Explanation / Answer

Given

R1 = 3 m and R2 = 4.5 m

Each disc iss 10 cm thick

Density = 20 kg/m3

a) moment of inertia of the composte disc = 1/2 MR^2

Assuming M1 = M2

So M = M1 + M2 = 66 + 66 = 132

and Radius R = R1 + R2 = 3 + 4.5 = 7.5

moment of inertia of the composte disc = 1/2 MR^2 = 1/2*132*7.5^2 = 3712.5 kgm^2

b) If M1 = 66 kg then assuming no angular acceleation results in the system

M1w^2 = M2w^2

Since angular accelartion is same, it mean M1 = M2

Therefore M2 = 66 Kg.

c) If 33 kg is added to M1 and M2

M1 = 33 Kg and M2 = 66 + 33 = 99

So then angular acceleartion of disc will be = 99/20*10/100 = 99/(20*10) = 0.495

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