Four identical particles of mass m are mounted at equal intervals on a thin rod

Question

Four identical particles of mass m are mounted at equal intervals on a thin rod of length l and mass M, with one mass at each end of the rod.

Part A
If the system is rotated with angular velocity omega about an axis perpendicular to the rod through one of the end masses, determine the kinetic energy of the system.
Express your answer in terms of the variables m, M, l, and omega.
K=

Part B
If the system is rotated with angular velocity omega about an axis perpendicular to the rod through one of the end masses, determine the angular momentum of the system.
Express your answer in terms of the variables m, M, l, and omega.
L=

Explanation / Answer

a)

Omega = W

The moment of Inertia of the system (rod+ masses) is
I = (Ml^2)/3 + m(l/3)^2+ m(2l/3)^2+ ml^2 = (3M+14m)*(l^2)/9.
kinetic energy of rod = 1/2 I*W^2 = (3M+14m)*(l^2)*(W^2)/18

b)
Angular momentum = I? = (3M+14m)*(l^2)*W/9

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