A muggle at NYU College finds the magic wand of a student at NYU's sister school, Hogwarts School of Witchcraft and Wizardry. She decides to use physics to figure out how to wield the wand. The student measures the wand to have total mass M and length L and draws a sketch of the wand below. She realizes that the wand is constructed to have an unusual mass density, which increases linearly from the lighter left side (x = 0) to the heavier right side (x = L).

1. If the student wanted to balance the wand horizontally on the tip of her finger, under which point on the sketch should she place her finger?

2. If the student tries to spin the wand perpendicular to its axis with one of these points chosen as the pivot, around which point will the rotational inertia be the greatest?

3. If the student wants to wave the wand around as easily as possible, should they grasp it at the left end or the right end?

4. To perform a particular spell, the student finds they need to flick the want by a particular angle in a particular time. Specifically, the wand must be rotated by 90 degrees in 0.5 seconds, starting from rest with a constant angular acceleration. What is the magnitude of the required angular acceleration?

1. 25 rad/s?
2. 13 rad/s?
3. 6.2 rad/s?
4. 3.1 rad/s?

A B C D E X=0 2L X= NIC X= X=L 3