The object shown below is composed of three masses attached by thin rods. Assume
ID: 1265072 • Letter: T
Question
The object shown below is composed of three masses attached by thin rods. Assume that the rods are massless. Moss 1 is 5.00 kg, mass 2 is 4.00 kg, and mass 3 is 3.00 kg. a) By direct calculation, find the rotational inertia (moment of inertia) of axis this object when it rotates about axis 1. b) By direct calculation, find the rotational inertia (moment of inertia) of this object when it rotates about axis 2. c) By direct calculation, find the rotational inertia (moment of inertia) of this object when it rotates about axis 3. d) Locate the center of mo of this object. e) By direct calculation, find the rotational inertia of this object when it rotates about an axis through the center of mass and parallel to the three axes shown in the picture f) Now use the parallel axis theorem to compare your answers to ports (a) arid (b) and (c). Direct calculation means using I as appropriate.
Explanation / Answer
a) I1 = m2*0.6^2 + m3*(0.5+0.6)^2 = (4*0.6*0.6)+(3*1.1*1.1) = 5.07 kg m^2
b) I2 = m1*0.6^2 + m3*(0.5)^2 = (5*0.6*0.6)+(3*0.5*0.5) = 2.55 kg m^2
c) I3 = m2*0.5^2 + m1*(0.5+0.6)^2 = (4*0.5*0.5)+(5*1.1*1.1) = 7.05 kg m^2
d) ycm = ((m2*0.6)+(m1*1.1))/(m1+m2+m3)
ycm = ((4*0.5)+(5*1.1))/(5+4+3) = 0.625 m from M3 in upward
e) I3 = Icm + (M*0.625^2)
Icm = 7.05-((5+4+3)*0.625*0.625) = 2.3625 kg m^2
f) I1 = Icm + M*(1.1-0.625)^2
I1 = 2.3625+(12*0.475*0.475) = 5.07 kg m^2
I2 = Icm + M*(0.625-0.5)^2
I2 = 2.3625+(12*0.125*0.125) = 2.55 kg m^2
I3 = Icm + M*(0.625)^2
I3 = 2.3625+(12*0.625*0.625) = 7.05 kg m^2