Mounted on a low-mass rod of length 0.52 m are four balls. Two balls each of mas

Question

Mounted on a low-mass rod of length 0.52 m are four balls. Two balls each of mass 0.89 kg, are mounted at opposite ends of the rod. Two other balls, each of mass 0.28 kg are each mounted a distance 0.13 m from the center of the rod. The rod rotates on an axle through the center of the rod perpendicular to the rod, and it takes 1.5 seconds to make one full rotation.

(a) What is the moment of inertia of the device about its center?

(b) What is the angular speed of the rotating device?

(c) What is the magnitude of the angular momentum of the rotating device?

Explanation / Answer

(a) What is the moment of inertia of the device about its center?

MI of complete system = MI of rod + MI of all the masses

=> 0 + 2*0.89*(0.26)^2 + 2*(0.28)*(0.13)^2 = 0.129792 kgm^2

(b) What is the angular speed of the rotating device?

=1/1.5 rev/sec = 2/1.5 rad/sec = 4.18 rad/s

(c) What is the magnitude of the angular momentum of the rotating device?

=>I = 0.129792*4.18=0.54253056 N·m·s

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