1. the earth spins one full rotation every 24 hours. you, a mad scientist bent on destroying the world, wish to make "earth stand still" - you want to make it stop rotating. in your arsenal, you have lots and lots of rocket engines that you are free to place however you wish around the earth. how will you arrange these rockets to stop the earth's rotation (where will you put them, how will you orient them)? how much total thrust will you need to stop the rotation? assume the earth is a uniform sphere. you can find the mass and radius of the earth, and you will need the moment of inertia through a sphere's center of mass, which you can also find on google.
2. when an object rolls without slipping, the static friction acts antiparallel to the direction of motion. why don't we usually worry about the (negative) work done by the static friction on the rolling body? hint: how does the rotational work done by the static friction compare? it will to set up an example problem and calculate the quantities explicitly to compare them.