Homework $10$: Rotational Dynamics

Torque: A Bent Pipe

A metal pipe consists of two identical pieces, each $150$ cm long and each with a mass of $2\mathrm{.}5$ kg $,$ that are joined at a $\backslash (150^\{\backslash$circ$\}\backslash )$ angle. This pipe is placed on a fulcrum at the place where the pieces are joined so that one side is horizontal and the other is angled down at $\backslash (30^\{\backslash$circ$\}\backslash )$ below the horizontal $($as shown in the figure$).$

A$)$ In this case, the pipe will not be in equilibrium. Find the net torque on the pipe, treating the fulcrum as the pivot point. Give a magnitude and a direction.

B$)$ Suppose that you want to hold the pipe in place by pushing down on the very end of the downward$-$angled section of the pipe. What force should you apply? Conservation of Angular Momentum: Jumping onto a Merry Go Round

Joey, mass $\backslash (=20\backslash$mathrm$\{$~kg$\}\backslash ),$ takes a running jump onto a moving merry$-$go$-$round. Before Joey jumps on it$,$ the merry go$-$round makes $0\mathrm{.}8$ rotations per second. If the merry$-$go$-$round is a disk with a mass of $85$ kg and a radius of $1\mathrm{.}5$ m $,$ find its rotational frequency after Joey lands on it if he runs directly toward the center of the merry go round with a speed $\backslash (2\mathrm{.}5\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$ and lands on a spot $1$ m from the center. You may treat Joey as a point$-$particle, I won't be offended.