Physics I – Test 3 Study Guide
What to Expect
The test is divided between concept questions, short calculations for which no work need be shown, and longer worked
problems for which you will show work and may receive partial credit.
You will have two and a half hours from when the materials are first posted to complete the test, though it is not
intended to take that long. This includes grace time to upload you work. Submissions received after the deadline without
extreme mitigating circumstances will take a 50% grade penalty.
The test is open book/note but you are not permitted to ask others for assistance (be they other students, academic
“sharing” sites, or anyone else) and must sign an honor statement to that effect. Students found to have received
unauthorized assistance on the test will receive a 0 and be reported to the College.
Preparation Tips
1. Go over homework, examples, and labs. Some similar questions/problems will appear on the test. Worked
examples and homework solutions are posted to Blackboard.
2. Review class lecture notes and lecture slides. Pay particular attention to the poll questions! Concept review
questions are also good preparation for the concept section of the test.
3. On a timed, open note exam, organization is key. It helps to make a quick reference sheet of useful equations,
methods, and concepts which we’ve used frequently in these chapters. The course equation list makes a good
starting point but is not comprehensive. Make sure you know the meanings and uses of equations on your list,
including appropriate units.
4. A practice exam with solutions will be posted before the test date. Working through this will provide extra
problem-solving experience and give you a sense of the test structure and pace.
5. Make sure to have a scientific or graphing calculator handy on test day!
6. If you have questions or concerns about any of the material, please talk to me before the test. Drop me an
email/text or make an appointment for a Collaborate meeting, I’m here to help!
During the Test
It’s important to manage your time well on the test!
• If you are stuck on a question or problem, move on and come back to it later.
• Don’t spend too long on the concept questions. These questions aren’t intended to take more than 20 – 30
minutes at most, the bulk of test time is needed for the problems.
• Never leave a blank answer! Any work is better than no work, and even an explanation in words of the main
physical ideas in the problem may be worth something.
• The time limit is intended to prevent you from being able to look up every answer! This is not a take-home test
with unlimited time, be sure to carefully budget and make sure you are proceeding through the test at a pace
that will allow you to finish. Good preparation will help!
Physics I – Test 3 Study Guide
Sections, Topics, and Methods to Covered:
Chapter 9 sections: 9.1 through 9.6
1. Elastic (KE conserved), inelastic (KE not conserved) and completely inelastic (colliders stick) collisions –
distinguished by conservation of kinetic energy, not momentum! Know that in a completely inelastic collision,
the final speed of the masses must be the same.
2. Momentum-Impulse Theorem: ?? = Σ�⃑�? Δ?? = Δ??. Be able to use this theorem to explain why maximizing the
time over which a momentum change occurs, or minimizing the change in momentum, is often desirable.
3. Remember that impulses form Third Law pairs, just like forces.
4. After using the Impulse-Momentum theorem to find a net force, be able to use a free body diagram and force
sum to isolate individual forces.
5. Momentum Conservation Principle: ???????? = constant if and only if ∑ �⃑�? = 0. That is, there is no net force on the
system. If true then: m1v�⃑ f1 + m2v�⃑ f2 + … = m1v�⃑ 01 + m2v�⃑ 02 + …
6. Energy and collisions: be able to find the kinetic energy retained or lost during a collision.
7. Momentum conservation in 2-dimensions (e.g., collisions or explosions), know how to detect situations where a
system conserves momentum on one axis but not the other.
8. How to identify and solve problems in which both momentum and energy interactions occur, such as ballistic
pendulums. These problems must be
oken down into two or more steps, during which either energy o
momentum is considered, with the final velocity of each step being the initial velocity of the next.
Chapter 10 sections: 10.1 through 10.6
• Definitions of angular displacement, velocity, and acceleration - be able to solve problems using the equations of
angular kinematics.
• Conversion between angular and tangential variables, and how this applies to rolling. Understand the
differences between angular and tangential variables.
• Moment of inertia: is to angular motion as inertial mass is to linear motion.
o Understand how the moment of inertia of a solid object changes with the distribution of mass and the
location and orientation of the axis of rotation. More mass further away from axis = larger I.
o Be able to directly calculate the moment of inertia of a collection of discrete masses.
o Be able to use the parallel axis theorem to determine the new moment of inertia when the axis is
moved.
o Note: you will need a moment of inertia table!
• The definition of torque. Be able to determine the torque caused by a force about an axis.
• Center of gravity/mass – the point where the force of gravity effectively acts on an object. For a uniform object,
this is its geometric center.
• Newton’s First Law as it pertains to rotational motion – a rotating object will remain at rest or in motion at
constant angular velocity unless compelled to change by a net torque.
• Newton’s Second Law: Σ?? = Ι�⃑�? and how to use it to solve non-equili
ium problems.
• Rotational work and power – analogous to their linear equivalents
Physics I – Test 3 Study Guide
Chapter 12 sections: 12.1 and 12.2
• Remember the condition for translational equili
ium: ΣFx = 0, and ΣFy = 0. This can be static or dynamic
(motion at constant velocity)
• Condition for rotational equili
ium, Σ??�⃑ = 0 about any axis. This can be static (no rotation) or dynamic (rotation
at a constant angular velocity).
• Be able to identify when each of these conditions applies. Know how to solve problems for the static case using
these conditions, and choosing an axis to eliminate one unknown.
Chapter 11 sections: 11.1 through 11.3
• Rolling motion – the motion at the axis is equivalent to the tangential motion at the rim
• Kinetic energy is the sum of both translational and rotational K, larger I means more energy is tied up in the
otational aspect
• Conservation of energy with rolling – be able to solve problems involving rotating without slipping and height
change (objects rolling on ramps, pulleys etc.).
• Vector nature of rotation - right hand rule to find the direction of an angular variable
• Cross product
o Know the rules and identities including the reference circle
o Be able to use right hand rule to find direction
• Definition of torque and angular momentum in terms of cross products
• Relation between net torque and change in angular momentum
o Be able to solve problems using this relation
• Angular momentum definition – constant (NOT generally zero) for linear motion
• Angular momentum conservation: occurs when Σ??�⃑ = 0 on the system.
o When moment of inertia changes, angular velocity changes: lots of examples
o Collisions – translation of linear to angular momentum
Sample Test 3 Name: _________________________
1. (5 pts) The center of mass of the system of particles shown in the diagram is at
point:
a) 1
) 2
c) 3
d) 4
e) 5
2. (6 pts) Two cars collide on a patch of ice. After the collision, they are locked together and move off as a single mass.
i. What kind of collision is this?
ii. Is the kinetic energy of the two cars together conserved? If so, why? If not, where does the energy go?
3. (6 pts) The linear momentum of a system is conserved if and only if…
a) all forces on that system sum to zero
) the work by non-conservative forces on the system is zero
c) friction and air resistance do no work on the system
d) conservative forces do work on the system
e) the internal forces between elements of the system cancel out
4. (8 pts) A wheel is rotating clockwise on a fixed axis perpendicular to the
page (x) as shown. The wheel is slowing down. For each quantity, identify
the vector which represents the direction of that quantity and write its
number (1, 2, 3, or 4) in the blank:
i. Angular velocity ______
ii. Angular acceleration ______
iii. Net torque ______
iv. Angular momentum ______
5. (6 pts) Five pucks slide across frictionless ice, and are subjected to forces as shown. Only one of these five pucks is in
equili
ium (both linear and rotational). Which one is it?
a) 1
) 2
c) 3
d) 4
e) 5
6. (6 pts total) Two children (Alice and Bob) are riding on a rotating me
y-go-round. Alice is at a greater distance from
the axis of rotation than Bob.
i. Which child has the larger tangential speed?
a) Alice
) Bob
c) They both have zero tangential speed.
d) They have the same non-zero tangential speed.
ii. Which child has the larger angular speed?
a) Alice
) Bob
c) They both have zero angular speed.
d) They have the same non-zero angular speed.
7. (6 pts total) Which of the two pictured objects has a larger moment of inertia, A B
assuming a vertical axis of rotation through the center of the object? Both objects have the same mass.
a) Object A
) Object B
c) Both objects have the same moment of inertia for this choice of axis.
Explain:
8. (6 pts) An airplane with a single propeller is flying through the air. From the perspective of the pilot, the propeller
otates clockwise. If the pilot points the plane’s nose downward to dive, the plane will…
a) veer to the left
) veer to the right
c) try to roll over
d) try to slow down
e) None of these is co
ect
9. (6 pts) An