Moments of Inertia/Center of Mass

  • #1
Could someone help me get started on these two types of problems? (In terms of what equations to use/what the problems are asking for or mean)

Moments of inertia
-A rigid body consists of 2 point masses m1= 1kg at a position vector r1= (1,2,3) m and m2 = 2kg at a position vector r2- (0,1,0) m. Calculate the moments of inertia of this body about the x, y and z axes.

-Four uniform solid spheres of equal mass M = 100 g and radius R = 3 cm are arranged in a square and rigidly connected by four rods of equal mass m = 30 g and length L = 10cm

a) calculate the moments of inertia of the system about the axis AB through the centers of the opposite sides of the square.
b) calculate the moments of inertia of the system about the axis A'B' through the vertices of the square.

(Figure is/looks like a square with A' at the top left, nothing marked at top right, M marked at bottom left and B' marked at bottom right. There is a dotted line in the center of the square marked A B and a diagonal dotted line across the square from points A' to B'. L is from M to B' and 2R is from the top of M to the bottom of M (imagine each vertices to be a sphere, therefore 2R is from the top of the sphere to the bottom).

Center of Mass
-Three point masses 30 g each are placed at the vertices of an equilateral triangle ABC and rigidly connected by three rods of length 10 cm. The Rods AB and AC have equal mass 50 g while the mass of the rod BC is 20 g.

Calculate the distance from the center of mass to the vertex A.

(Figure of Triangle has A vertex at top, C at the bottom left and B at the bottom right)

I have no idea how to get started on the Moments of Inertia problem, in fact if you could explain what exactly the problem is looking for that'd be great; but for the center of mass problem I know the equation is m1x1+m2x2+m3x3/m1+m2+m3 but I don't know what x is and how to use the mass of the rods in the equation...

Again any help would be extremely useful :smile:
 

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