Physics Final Exam Written Problems.

$1.$ Christmas Elf Jim is standing on a north pole merry go$-$round, and due to the iciness of the situation and the silly elf shoes he's wearing, there is only a coefficient of static friction of $0\mathrm{.}15$ between his shoes and the deck of the merry go round.$$ Christmas Elf Tim has got Jim going at a pretty good angular velocity of $3\mathrm{.}0$ radians per second.$$ Use the ideas of centripetal acceleration, force, and friction to determine how far out from the center of the merry go round Jim could stand without sliding and being thrown off.

$2.$ Christmas Elf Tim loves to ice skate on a little circular frozen pond of a DIAMETER $30$ meters.$($Please recall diameter is different from radius!$)$ He can really move on his magic elf skates, circling the outer perimeter of the pond with a linear speed of v$=10$ meters per second.$$ Use the idea of centripetal acceleration and related analysis of forces to find the bank angle at which he would be tilted up above the ground level to achieve this elven miracle.