A uniform bar has two small balls glued to its ends. The bar is 2.30 m long and

Question

A uniform bar has two small balls glued to its ends. The bar is 2.30 m long and with mass 2.10 kg , while the balls each have mass 0.500 kg and can be treated as point masses.

A Find the moment of inertia of this combination about an axis perpendicular to the bar through its center

. B. Find the moment of inertia of this combination about an axis perpendicular to the bar through one of the balls.

C. Find the moment of inertia of this combination about an axis parallel to the bar through both balls.

Explanation / Answer

for 1,2, and 3 take the individual moments and add them together.

For 4, use the parallel axis theorem.

1. for the bar I=m*L^2/12=2.1*9/12= 1.57
for the point masses
3*(0.500)*1.5^2=2.03 add them together
= 3.375

2) for the bar
I=m*L^2/3=2.1*(2.3)^2/3= 3.703
for the point masses
I=m*L^2/3=(0.500)*(2.3)^2/3=0.881

add them together
9

3) If the rod has 0 diameter, then the moment is 0

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