Rotational Motion;
Introduction
In this lab a constant torque will create a constant angular acceleration for a rigid body rotating
about its center of m
ass. You will see that the moment of inertia depends on the rotation axis for
a given object and finally you will look at ro
tational motion from an energy viewpoint.
Applications of the moment of inertia concept include the design of crankshafts, rotary rides at a
fair, or the baton twirling of a marching band
leader. Text Reference: Young & Freedman § 9.1-
5.
Theory
A stone dropped into a well falls a distance
2
2
1
tgy
?=?
. If we convert this equation to the
angular dom
ain by considering a disk turning about some axis it says
2
2
1
t
?=?
a?
.
In more detail, a rigid object free to rotate about a principle axis with moment of inertia
I
will
accelerate according to
where
t
is the net torque (given by the sum of
Fr
×
for each force applied to the object), and
a
is the angular acceleration in rad/sec
2
. Recall
p
radian = 180
°
. Take care that
t
,
a
, and
I
are in
consistent units. The moment of inertia
I
is readily calculated for symmetric objects, and has the
form
I
=
ß
MR
2
, where
ß
is a dimensionless fraction between 0 and 1 that depends on the shape of
the object and the rotation axis. A 3-dimensional object has three principal values of
I
,
corresponding to three independent possible axes of rotation. These values would all be the
same for a sphere through its center, but all three values would be different for a low symmetry
object. Thus, for example, a rectangular block of dimensions
a
×
b
×
c
has moment of inertia
for rotation about the axis normal to the
a
×
b
face and passing through its center.
In this lab, we use the arrangement shown in figure 1. A rectangular block of mass
M
and
dimensions
a
×
b
×
c
is mounted with a rotation axis through the center of one face. A mass
m
is
tied to a string wound around a massless pulley of diameter 2
r
mounted on the same axis. The
string exerts a torque on
M
given by
where
T
is tension in the string which can be found using Newton’s second law and is
Note we have used
a
=
a
r
, and both
g
and
a
are positive. Combining these equations we have
(
)
1
a
t
I
=
(
)
()
2
12
1
22
baMI
+
=
(
)
3
rT
=
t
(
)
(
)
(
)
4
.
rgmagmT
a
–
=
–
=
where we have written
I
d
(dynamic moment of inertia) to distinguish it from the static moment of
inertia
I
s
determined from the geometry and mass, as in equation 2. These are entirely equivalent
in principle.
Figure 1. Apparatus for the dynamic measurement of rotational moment of inertia.
It is also useful to look at this problem
from an energy viewpoint. Thus we have
and for our specific problem this can be written as
where
?
and
?
are the angular velocity and position of the pulley. The terms in
m
and
?
are due
to the kinetic energy of the small mass as it falls. To get the signs right, note that the change in
height
?
h
is negative, and the change in potential energy is negative. Note that the kinetic
energy includes both the spinning block (
M
) and the falling mass (
m
), while the potential energy
involves only the falling block, and all terms can be written in terms of pulley angle, as above.
Think about the signs of the two terms in equation 7 needed to keep the sum zero.
Procedure
()
5
?
?
?
?
?
?
–
=
a
a
rg
mrI
d
(
)
6
0
=
?
+
?
UK
()
(
)
(
)
()
7
0
2
1
222
=+-+-
+
if
if
s
mgr
mrI
??
??
2r
m
M
rotation axis
4. Research Statement will be attached. It is actually my paper in process. You will have a better idea how the format will be.
LAB REPORT GUIDLINESS
Lab Report is written from the third person; in the passive form, in the past tense. Signed data sheets
need to be stapled to the back of the report. All graphs must be labeled.
Lab report without the signed data sheets attached will automatically get a zero score.
Lab Report includes the following parts, each of them needs to be clearly marked in the lab report:
Title of the experiment; Student’s name (prominent); lab partners’ names; Group Number (attached to the lab
computers); TA’s name; Section number (SLN number from ASU catalog). (1 point)
Objective section – (3 points) It is a statement of what physics concepts/theory/law was investigated or tested.
What physics quantities had to be measured? It is one or two sentences.
Experimental Data (3 points)– raw data collected during the lab experiment. All experimental data should be
tabulated. Tables should have appropriate headings and contain units. All plots should be clearly labeled and scales
adjusted to present graph appropriately.
Data analysis section – (10 points)
The section where the experimental data used to calculate the physics quantity that needs to be found to achieve
the objective. All necessary calculations have to be present, which also includes all equations. All intermediate
quantities are also provided. All the work for calculating uncertainties of the experiment is also present.
Microsoft equation is one of the tools that can be used for typing the equation. The equation can either be typed
or it will also be acceptable to neatly hand write these calculations.
Results section – (3 points)
Results must be tabulated. Results include the physics quantities that were stated to be found in the objective. The
results should be organized in clearly labeled tables along with their errors if applicable. Results and uncertainties
have to be reported with the correct number of significant figures and appropriate unit.
The raw experimental data collected during the lab and signed is not what needs to be reported in the result
section.
Discussion and Conclusion section – (10 points)
This is the most important part of the lab report. Begin discussion with the purpose of the experiment. Briefly
explain the physics theory/concept that was tested. State only the key results (with uncertainty and units)
quantitatively with numerical values; does not provide intermediate quantities.
Briefly explain the procedure that was used to collect the experimental data. Describe difficulties and
shortcomings that were encountered during the experiment and it caused the uncertainties in the final results.
Discuss “statistical errors” that affect your measurements, but which you can’t do anything about given the time
and equipment constraints of this laboratory. Suggest experimental redesigns to eliminate and overcome these
troubles. Include a description of sources of “systematic errors” in your measurement that bias your result (e.g.
friction in pulleys that are assumed frictionless in the formula). Describe the qualitative effect of each source of
error (e.g. friction slowed motion, causing a smaller value of acceleration to be measured). Describe only the 5
prominent sources of error in the experiment.
Address questions such as: Are the deviations in the experimental results due to uncertainty in the
experimental method, or are they due to idealizations inherent in the theory (or both)? If the deviations are due to
experimental uncertainties, can you think of ways to decrease the amount of uncertainty? Discuss how the
apparatus could be redesigned to reduce uncertainties or to streamline experimental technique. If the deviations
are due to idealizations in the theory, what factors has the theory neglected to consider?
All questions from the Lab Manual should be also answered in the discussion section. The conclusion
made if the objective of the experiment achieved.
Overall the full lab report is expected to be about 4-5 pages.
PLACE THIS ORDER OR A SIMILAR ORDER WITH US TODAY AND GET AN AMAZING DISCOUNT ?
Our Service Charter
-
Excellent Quality / 100% Plagiarism-Free
We employ a number of measures to ensure top quality essays. The papers go through a system of quality control prior to delivery. We run plagiarism checks on each paper to ensure that they will be 100% plagiarism-free. So, only clean copies hit customers’ emails. We also never resell the papers completed by our writers. So, once it is checked using a plagiarism checker, the paper will be unique. Speaking of the academic writing standards, we will stick to the assignment brief given by the customer and assign the perfect writer. By saying “the perfect writer” we mean the one having an academic degree in the customer’s study field and positive feedback from other customers. -
Free Revisions
We keep the quality bar of all papers high. But in case you need some extra brilliance to the paper, here’s what to do. First of all, you can choose a top writer. It means that we will assign an expert with a degree in your subject. And secondly, you can rely on our editing services. Our editors will revise your papers, checking whether or not they comply with high standards of academic writing. In addition, editing entails adjusting content if it’s off the topic, adding more sources, refining the language style, and making sure the referencing style is followed. -
Confidentiality / 100% No Disclosure
We make sure that clients’ personal data remains confidential and is not exploited for any purposes beyond those related to our services. We only ask you to provide us with the information that is required to produce the paper according to your writing needs. Please note that the payment info is protected as well. Feel free to refer to the support team for more information about our payment methods. The fact that you used our service is kept secret due to the advanced security standards. So, you can be sure that no one will find out that you got a paper from our writing service. -
Money Back Guarantee
If the writer doesn’t address all the questions on your assignment brief or the delivered paper appears to be off the topic, you can ask for a refund. Or, if it is applicable, you can opt in for free revision within 14-30 days, depending on your paper’s length. The revision or refund request should be sent within 14 days after delivery. The customer gets 100% money-back in case they haven't downloaded the paper. All approved refunds will be returned to the customer’s credit card or Bonus Balance in a form of store credit. Take a note that we will send an extra compensation if the customers goes with a store credit. -
24/7 Customer Support
We have a support team working 24/7 ready to give your issue concerning the order their immediate attention. If you have any questions about the ordering process, communication with the writer, payment options, feel free to join live chat. Be sure to get a fast response. They can also give you the exact price quote, taking into account the timing, desired academic level of the paper, and the number of pages.