Physics 3221 Spring Term 2007 Test 1, February 7, 2007

Physics 3221
Spring Term 2007
Test 1, February 7, 2007
• This is an open notes/text book/Homework test lasting 50 minutes.
• There are 4 problems, divided into subsections. The points for each part are
• Begin each problem on a fresh sheet of paper. Use only one side of a
sheet of paper.
• Put your name, the problem number, and the page number in the upper
right hand corner of each sheet.
• To receive partial credit you must explain what you are doing. Carefully
labeled figures are important. Randomly scrawled equations aren't helpful.
• Draw a box around important results.
There are 2 pages including this page. Do not forget to look at all parts of the
1. (4 points) A guitar string has mass m, length l and the tension T. (Tension has the same
dimension as force.) Wave travels with velocity v ∝ m a l bT c on the string. Find a, b and c.
a) (3 points) The following matrix is a valid rotation matrix. Find the values and
signs of a and b.
⎛ 0 .6 a 0 .8 ⎞
⎜ 0 1 0 ⎟
⎜ 0. 8 0 b ⎟
b) (1 point) Point P is at position x=1, y=2, z=3 in the original coordinate system.
Find its new position after the axes are rotated according to the rotation matrix in part (a).
3. Find a normal for the following surfaces
a) (2 points) x2y2-z3 = 4 at the point (1,2,0).
b) (3 points) z = x2-y2 at the point (2,1,3).
4. In the following figure, Points A and C are vertices of the unit cube. Point B is the
midpoint of one of the edges.
a) (2 points) Find the angle between AB and BC.
b) (2 points) Find the unit normal to plane ABC.
c) (3 points) Find the distance from the origin to plane ABC.