Two masses m1 and m2 are attached to a rod that is capable of rotating about an

Question

Two masses m1 and m2 are attached to a rod that is capable of rotating about an axis perpendicular to the rod and passing through the end A as shown in the diagram below. The length of the rod is L = 18.0 cm, m1 = 2.00 g, m2 = 3.50 g, x1 = 6.10 cm and x2 = 8.05 cm.

(a) What is the moment of inertia of the system about the specified axis if the rod's mass is negligible?
____ kg · m2

(b) What is the moment of inertia of the system about the specified axis if the rod has a mass of 8.00 g?
____ kg · m2

Explanation / Answer

Given

masses m1 = 2.0 g , m2 = 3.5 g at

x1 = 6.10 cm, x2 = 8.05 cm

lengthof the rod L = 18 cm

mass of the rod m = 8 g

a) moment of inertia of the system is

I_a = m1*x1^2+m2*x2^2

I_a = 2*10^-3*(6.10*10^-2)^2 + 3.5*10^-3*(8.05*10^-2)^2 kg.m^2

I_a = 3.0123*10^-5 kg m2

b)

moment of inertia of the systenm when the rod rotating about the axis passign through one end

moment of inertia of the rod is I1 = 1/3*M*L^2

total moment of inertia is I = I1+ I_a

I = (1/3*M*L^2)+ (m1*x1^2+m2*x2^2)

I = (1/3*8*10^-3*0.18^2)+3.0123*10^-5 kg m^2

I = 0.000116523 kg m^2

i = 0.116523*10^-3 kg m^2

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