Two masses m 1 and m 2 are attached to a rod of negligible mass that is capable

Question

Two masses m1 and m2 are attached to a rod of negligible mass that is capable of rotating about an axis perpendicular to the rod and passing through the end, A, as shown in the diagram below. The length of the rod is

= 16.0 cm,

m1 = 3.00 g,

m2 = 4.50 g,

x1 = 1.80 cm,

and

x2 = 7.40 cm.

If the rod rotates clockwise in the x-z plane with an angular speed of 5.00 rad/s, what is the angular momentum of the system? We use the standard rectangular coordinate system with +x axis to the right, +y axis vertically up, and +z axis coming out toward you. Enter your answer using unit vector notation.

kg · m2/s

Explanation / Answer

m1 = 3.00 g = 0.003 kg

m2 = 4.50 g = 0.0045 kg

x1 = 1.80 cm = 0.018 cm

x2 = 7.40 cm = 0.074 cm

Total moment of Inertia of System about the rotation axis through A is given by

IA= m1x12 + m2(x1+x2)2 = 0.003 (0.018)2 + (0.045) { (0.018)2 + (0.074)2 } = 2.56 x 10 -9 kg.m2

Total Angular Momentum = Moment of Inertia x Angular velocity = 2.56 x 10 -9 x (-5) kg.m2/s = - 12.8 kg.m2/s

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