Mounted on a low-mass rod of length 0.44 m are four balls. Two balls (shown in r

Question

Mounted on a low-mass rod of length 0.44 m are four balls. Two balls (shown in red on the diagram), each of mass 0.62 kg, are mounted at opposite ends of the rod. Two other balls, each of mass 0.29 kg (shown in blue on the diagram), are each mounted a distance 0.11 m from the center of the rod. The rod rotates on an axle through the center of the rod (indicated by the "x" in the diagram), perpendicular to the rod, and it takes 1.3 seconds to make one full rotation.

Mounted on a low-mass rod of length 0.44 m are four balls. Two balls (shown in red on the diagram), each of mass 0.62 kg, are mounted at opposite ends of the rod. Two other balls, each of mass 0.29 kg (shown in blue on the diagram), are each mounted a distance 0.11 m from the center of the rod. The rod rotates on an axle through the center of the rod (indicated by the x in the diagram), perpendicular to the rod, and it takes 1.3 seconds to make one full rotation. (a) What is the moment of inertia of the device about its center? I= ___kg.m^2 (b) What is the angular speed of the rotating device? omega = _____ radians/s (c) What is the magnitude of the angular momentum of the rotating device? |L|= ______kg.m^2/s

Explanation / Answer

(a)
The rod doesn't have mass or inertia.
So just the balls
Inertia of 2 balls 0.22 m from the centre, I1 = 2 * 0.62 * 0.22^2
I1 = 0.06 kgm2

For the other two, Inertia, I2 = 2 * 0.29 * 0.11^2
I2 = 0.007 kgm2

Total Inertia, I = I1 + I2 = 0.06 + 0.007
I = 0.067 kgm2

(b)
w = 2pi/t
w = 2pi/1.3
w = 4.83 rad/s

(c)
L = Iw
L = 0.067 * 4.83
L = 0.324 kgm2/s

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