Mounted on a low-mass rod of length 0.32 m are four balls. Two balls (shown in r

Question

Mounted on a low-mass rod of length 0.32 m are four balls. Two balls (shown in red on the diagram), each of mass 0.56 kg, are mounted at opposite ends of the rod. Two other balls, each of mass 0.25 kg (shown in blue on the diagram), are each mounted a distance 0.08 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 1.0 seconds to make one full rotation. What is the moment of inertia of the device about its center? What is the angular speed of the rotating device? What is the magnitude of the angular momentum of the rotating device?

Explanation / Answer

Part a

moment of inertia

I = moment of inertia of red balls+ moment of inetria of blue balls

I = m(L/2)^2 + m(L/2)^2 +M(0.08)^2 +M(0.08)^2

I = 2*0.56*(0.32/2)^2 + 2*0.25(0.08^2)

I =0.028672 + 0.0032

I =0.031872kg-m^2

Part B

angular speed= angle/time

1 revolution in 1 second so

w = 2*pi/1

w = 6.28rad/s

Part C

angular momentum

L = I*w

L = 0.031872 * 6.28

L = 0.20015 kg-m^2/s

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