Problem 4: A 4 kg particle at (4,-2,-3) (all in meters) moves in the positive-z

Question

Problem 4: A 4 kg particle at (4,-2,-3) (all in meters) moves in the positive-z direction with a speed of 5 m/s. What is the angular momentum vector about the the position (0,1.2)? (8 points) Problem 5: A small merry go round at the park is rotating at 1.0 rad/s before a small child jumps on. The child is 40 kg and the radius of the merry go round is 1.5 m. If the child lands at a point halfway to the center, what is the an- gular speed of the system after she lands? Assume the merry go round to be a solid disc with mass of 100 kg. (8 points) Problem 6: An object of small mass is given a speed vo at a height h above a spherical planet with mass M and

Explanation / Answer

We will apply here the angular momentum conservation-

[I* (Omega)]i = [I* (Omega)]f

MR2/2 (Omega)1 = [MR2/2 + (40)(1.5/2)2] (Omega)2

100(1.5)2 /2 (1) = [100(1.5)2 /2 + (22.5)] (Omega)2

(Omega)2 = 112.5 / 135

(Omega)2 = 0.833 rad/s

Thank you !!! Have fun

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