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Particle mechanics in college physics (explanation)
Question 8, rotation theorem: M=Ia, vertical position, M=0, so a=0.

Angular velocity can be obtained by kinetic energy theorem, mgh = 0.5 iw 2, and h is the distance of falling center of gravity.

The supporting force can make the center of mass move in a circle.

Question 9: Divide the rod into segments and calculate the total torque generated by each point with calculus.