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A sewer pipe rolls more slowly down an incline than a bowling ball with the same mass. Understand this and more by learning about Moment of Inertia, a measure of how compact objects are.

As we saw in the previous problem, whomever worked on the pyramid moved a tremendous amount of stone from the quarries. Let's ignore the effort it took to get the stone from the quarry to the pyramid site, since we don't know the distance, how far they could travel by water vs. cart, etc. and just look at how much effort it took to lift that mass off the ground. To answer this question, we need to know the height of the center of mass of a uniform pyramid with the dimensions of the great pyramid: 150 m high and 230 m on a side. For such a pyramid, how high off the ground is the center of mass **in m**?

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I assume that you work through these problems using some sort of writing utensil. Take your pen, balance it on its tip, and let go. It falls over. How fast in **m/s** is the other end of the pen going when it hits the table, assuming the tip doesn't slip? Take the pen to be a uniform one dimensional rod of length 15 cm.

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A picture is attached to a wall by two nails in the upper corners (these nails are at the very corners and also at the same height). The picture is wider horizontally than it is tall. Suddenly, one of the nails comes loose and so loses contact with the wall. If right after that moment, the y-component of the force acting on the picture by the other nail (still in contact with the wall) is unchanged, find the ratio of the horizontal width to the vertical height of the picture.

**Details and assumptions**

- The acceleration of gravity is \(-9.8~\mbox{m/s}^2\).

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**in Newtons** acting on the tip of the top.

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