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
marked.
• 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
problems.
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.
2.
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.
z
1
A
1
C
y
B
x
1
1/2
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.