Problem 9.31 A uniform bar has two small balls glued to its ends. The bar is 2.2

Question

Problem 9.31 A uniform bar has two small balls glued to its ends. The bar is 2.20m long and with mass 2.40kg , while the balls each have mass 0.600kg and can be treated as point masses. Part A: Find the moment of inertia of this combination about an axis perpendicular to the bar through its center. Part B: Find the moment of inertia of this combination about an axis perpendicular to the bar through one of the balls. Part C: Find the moment of inertia of this combination about an axis parallel to the bar through both balls.

Explanation / Answer

Moment of inertia of the bar about an axis perpendicular to the bar through its end=Ie=ML^2/3 Ie=4*2*2/3=16/3=5.333 kgm^2 moment of inertia of the ball through which axis passes is zero moment of inertia of the other ball about an axis through the other end of bar=Ib=mr^2=mL^2 moment of inertia of the other ball =Ib=0.5*2^2= 2 kgm^2 the moment of inertia of this combination about an axis perpendicular to the bar through one of the balls=I1=5.33+2=7.33 kgm^2

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