Two lightweight rods d = 28 cm are mounted perpendicular to an axle and at 180 T

Question

Two lightweight rods d = 28 cm are mounted perpendicular to an axle and at 180

Two lightweight rods d = 28 cm are mounted perpendicular to an axle and at 180 degree to each other. (see figure). At the end of each rod is a 610 g mass. The rods are spaced 40 cm apart along the axle. The axle rotates at 30 rad/s. What is the component of the total angular momentum along the axle? What angle does the vector angular momentum make with the axle? [Hint: Remember that the vector angular momentum must be calculated about the same point for both masses, which could be the CM.]

Explanation / Answer

We know L = I*w
Where L is angular momentum, I is rotational inertia, and w (omega) is angular velocity.

a) To calculate I, consider only the two masses. The axis rod does not contribute to the inertia because it is the axis, and the perpendicular rods are "lightweight" meaning they have no mass. The equation for I of mass at a distance (d) is Md^2.

So I = 2*M*d^2 and you are given omega.

b) To obtain the angle, simply draw a triangle from each mass to the center of mass of the axis. This forms a triangle with legs 21cm and 20cm.

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