Four point masses form a rigid body ( they are connected by massless rigid rods)

Question

Four point masses form a rigid body ( they are connected by massless rigid rods) given the positions of the individual masses below f M1 =3kg (2m, 4m,0m) M2=2kg (1m,-4m,0m) M3=1kg (10m,2m,0m) M3=5kg (-5m,2m,0m) Find: a) moment of inertia of this system when it rotates about x axis b) moment of inertia of this system when it rotates about y axis c) total rotational kinetic energy in the (a)case when angular velocity is 4rad/s d) total rotational kinetic energy in the case 9b) when angular velocity is 4rad/s For full marks show the small diagram of this situation as well as the symbolic formula used and the final answer

Explanation / Answer

He did a similar problem to this in the morning lecture on monday (but with 3 rods in the x,y & z axes). Ix= I1+I2+I3+I4= 1/12 [ m1l1^2+m2l2^2+m3l3^2+m4l4^2] where every l is the distance from the mass to the x axis (so only the y value of the coordinate) Iy is the same concept as Ix, except the distance L is from the mass to the y axis (which is just the x value of the coordinate) c) & d) are in our textbook, in the solutions manual p.176 &177 #25.

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