1. Physics I Name:____________________________________
Dr. Kirtland Date:_____________________________________
Exam Three Review Sheet
Directions: The following review sheet should not be taken as an exact replica of the exam. This
sheet is extra questions for practice and should be treated as so. The test will not be limited to
these problems and could possibly include other problems. Do not limit yourself to only studying
this sheet. Reference your homework, reading notes, and in class notes for more study material.
Answer the following questions on a separate sheet of paper and SHOW ALL WORK when computing
a problem. Be thorough with your description, this can lead to easy points on the exam if you
understand the concepts. Good luck, you can do this! ☺
1. Vectors: Given the following definitions of a cross product,
⃗A×⃗B=(Ay Bz−Az By) ̂x+(Az Bx−Ax Bz) ̂y+( Ax By−Ay Bx) ̂z=∣⃗A∣∣⃗B∣sinθ ,
compute the following:
a. If ⃗A=6 ̂x−3 ̂y+2 ̂z and ⃗B=2 ̂x+̂y−8 ̂z , find ⃗A×⃗B .
b. If ∣⃗A∣=12 , ∣⃗B∣=6 , and θ=45ο
, find ⃗A×⃗B .
2. Angular quantities: What are the following symbols given by:
a. angular position: _____
b. angular velocity: _____
c. angular acceleration: _____
What are the following formulas given by:
d. How do we relate angular position and angular velocity? ____________________________
e. How do we relate angular acceleration and angular velocity? _________________________
f. How do we relate angular acceleration and angular position? _________________________
g. How do we relate arc length and angular position? _________________________________
h. How do we relate angular velocity and translational velocity? ________________________
I. How do we relate angular acceleration and translational acceleration? __________________
3. Moment of Inertia: Calculate the moment of inertia for the following:
a. A uniform rigid rod of length L and mass M about an axis perpendicular to the rod and passing
through its center of mass. (Left figure below).
b. A uniform solid cylinder has a radius R, mass M, and length L rotating about its central axis (center).
(Right figure below).

2. 4. Torque: A block of mass M 1=2 kg and a block of mass M 2=6 kg are connected by a massless
string over a pulley in the shape of a solid disk having a radius R=0.250m and a mass M =10kg
. The fixed, wedge-shaped ramp makes an angle of θ=30ο
as shown below. The coefficient of
kinetic friction is 0.360 for both blocks.
a. Draw Free Body Diagrams for both blocks and the pulley.
b. Find the acceleration of the two blocks.
c. Find the tensions in the stings on each side of the pulley.
5. Angular Collision: A disk of mass, m, traveling at a velocity of, vi , strikes a stick of mass, M, of
length, L, that is lying flat on frictionless ice as shown below. The disk strikes at the end point of the
stick, at a distance, r, from the stick's center. The moment of inertia of the stick is given by, I. After the
collision, the disk is moving at a velocity of, v f , the stick is translating at a velocity of, V f , and
the stick is rotating with an angular velocity of, ω . The disk does not deviate from its original line
of motion.
Let's begin by setting up the problem:
a. Write an expression involving all of our unknowns above using conservation of linear momentum.
b. Write an expression involving all of our unknowns above using conservation of angular momentum.
Given the following quantities,
m=2kg ,vi=3
m
s
,M =1kg , L=4m ,r=2m , I =1.33kg m
2,
v f =2.3
m
s
c. Find ω and vsf .
d. From the information above, is this collission elastic? Explain how you got to this conclusion.

3. 6. Statics: A 1000 kg shark is supported by a rope attached to a 4.0 m rod with its pivot at the base as
shown in the diagram below. Ignore the weight of the rod.
a. Calculate the tension in the cable between the rod and the wall.
b. Find the horizontal force exerted on the base.
c. Find the vertical force exerted on the base.
7. Angular Momentum: A student sits on a freely rotating stool holding two dumbbells, each of mass
2.0 kg. When his arms are extended horizontally the dumbbells are 1.0 m from the axis of rotation and
the student rotates with an angular speed of 0.75
rad
s
. The moment of inertia of the student plus the
stool is 3.0 kg m
2
and is assumed to be constant. The student pulls the dumbbells inward horizontally
to a position 0.30 m from the rotation axis.
a. Find the new angular speed of the student.
b. Find the kinetic energy of the rotating system before and after he pulls the dumbbells inward.