Three light rods or negligible mass are joined to form an equilateral triangle o

Question

Three light rods or negligible mass are joined to form an equilateral triangle of length L = 2.00 m. Three masses m_1 = 5.00 kg, m_2 = 6.00 kg, and m_3 = 3.00 kg are fixed to the vertices of this triangle as shown in the diagram below. Treat the masses as point particles. What is the moment of inertia of the system about an axis lying in the plane of the triangle, passing through the midpoint of one side and the opposite vertex as shown by the dashed line? What is the midpoint of inertia of a mass m located a distance r from the axis of rotation? Which masses mit contribute is the of inertia of the system? kg middot m^2 What is the moment of inertia of the system about an axis passing through the center of the triangle and perpendicular to its plane? Review geometric properties of an equilateral triangle. What is the distance of each mass from the center of the triangle? kg middot m^2

Explanation / Answer

here,

m1 = 5 kg , m2 = 6 kg

m3 = 3 kg

L = 2 m

a)

the moment of inertia , I1 = m1 * (l/2)^2 + m2 * ( l/2)^2

I1 = ( 5 + 6 ) * 1^2

I1 = 11 kg.m^2

b)

the moment of inertia about an axis passing through the centre , I2 = m1 * r^2 + m2 * r^2 + m3 * r^2

I2= ( m1 + m2 + m3) * ( 1.15^2)

I2 = 18.6 kg.m^2

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