Four balls are mounted on a low-mass rod of length 0.52 m. Two balls (shown in r

Question

Four balls are mounted on a low-mass rod of length 0.52 m. Two balls (shown in red on the diagram), each of mass 0.66 kg, are mounted at opposite ends of the rod. Two other balls, each of mass 0.38 kg (shown in blue on the diagram), 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 (indicated by the "x" in the diagram), perpendicular to the rod, and it takes 1.0 seconds to make one full rotation.

(a) Calculate the moment of inertia of the device about its center.
I = ?
(b) Calculate the angular speed of the rotating device.
w = ?
(c) Calculate the magnitude of the angular momentum of the rotating device.

Explanation / Answer

(a)
Length of the rod,L = 0.52 m
Mass of each redball, m = 0.66 kg
Mass of each blueball, M = 0.38 kg
Distance of each red ball from the center, x = L / 2 = 0.26 m
Distance of eachblue ball from the center, y = L / 4 = 0.13 m
Moment of inertia,I = m r 2= 2 m x 2 + 2 M y 2
= 2*0.66*0.26^2 + 2*0.38*0.13^2
= 0.102076 kg m^2

(b)
Time period, T = 1 s
1 rotation =2 radians
Angular speed, = 2 / T
= 2 / 1
= 6.28 rad/s

(c)

Angular momentum, L = I
= 0.102076*6.28
= 0.64 kg m2 /s

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