Three point masses are fixed to an x-y coordinate system. A point \"m\" is place

Question

Three point masses are fixed to an x-y coordinate system. A point "m" is placed at the location (2,3), "2m" is placed at (3,0) and "5m" is placed at (-3,-4).

a.Determine the x position of the center of mass

b. determine the y position of the center of mass.

c.Determine the moment of inertia about the x axis

d.determine the moment of inertia about the y axis

e. determine the moment of inertia about the z-axis

f. determine the moment of inertia about the line y=x.

If you could use some explanation I would really appreciate it!

Explanation / Answer

Here ,

a) for the x position of the centre of mass is x

x = (m1 * x1 + m2 * x2 + m3 * x3)/(m1 + m2 + m3)

x = (m * 2 + 2m * 3 - 3 * 5m)/(m + 2m + 5m)

x = -0.875

the x position of centre of mass is -0.875

b)

Now , y position of centre of mass is

y = (m1 * y1 + m2 * y2 + m3 * y3)/(m1 + m2 + m3)

x = (m * 3 + 2m * 0 - 4 * 5m)/(m + 2m + 5m)

x = -2.125

the y position of centre of mass is -2.125

c) for the moment of inertia about x axis

Ix = m * 3^2 + 2 m * 0^2 + 5m *(-4)^2

Ix = 89 * m Kg.m^2

d)

for the moment of inertia about y axis

Iy = m * 2^2 + 2m * 3^2 + 5m * 3^2

Iy = 67 *m Kg.m^2

the moment of inertia about the y axis is 67 *m Kg.m^2

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