Two objects of different masses are joined by a light rod. a) Is the moment of i
ID: 1470853 • Letter: T
Question
Two objects of different masses are joined by a light rod.a) Is the moment of inertia about the center of mas the minimum or maximum and why?
b) If the two masses are 3kg and 5kg and the length of the rod is 2m, what are the moments of inertia of the system about an axis perpendicular to the rod, through the center of the rod and the center of mass?
Two objects of different masses are joined by a light rod.
a) Is the moment of inertia about the center of mas the minimum or maximum and why?
b) If the two masses are 3kg and 5kg and the length of the rod is 2m, what are the moments of inertia of the system about an axis perpendicular to the rod, through the center of the rod and the center of mass?
Explanation / Answer
a) The moment of inertia about the center of mass is the minimum.
b) let m1 = 3 kg
m2 = 5 kg
r = 2 m
distance from center of mass to m1, r1 = r*m2/(m1+m2)
= 2*5/(3+5)
= 1.25 m
distance from center of mass to m2, r2 = r*m1/(m1+m2)
= 2*3/(3+5)
= 0.75 m
moments of inertia of the system about an axis perpendicular to the rod, through the center of the rod and the center of mass,
I = m1*r1^2 + m2*r2^2
= 3*1.25^2 + 5*0.75^2
= 7.5 kg.m^2
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