Disk
Bolts
Object:
ENG252 Dynamics
PRACTICAL 3
Practical learning, for fun and credit
Practical 3
( Real life rigid-body motion
( Real life torsional vi
ation
( Group-work
( Calculations for a purpose (moment of inertia and natural frequency)
( Understanding the physical world
Your Jo
Your job in experiment 3 is to explore rigid body motion, moment of inertia and vi
ations using a “Trifilar” rig.
Context
Googling “trifilar” will show you where other universities have used this elegantly simple piece of classic engineering equipment. With it you can find polar moment of inertia (or radius of gyration) of complicated items such as motor vehicles (polar moment of inertia is needed in analyses of vehicle handling).
The rig gets its name from the way the test object (a circular disk with test items on it in this case) is suspended by three threads or “filaments”, hence tri-filar.
Schedule
Prac 3 (Lab 1)
Measure dimensions of the rig, do tests with a bare disk, explore the effects of adding mass to the disk, test a known object to find radius of gyration.
After Prac 3
Do calculations, develop a prediction method, discuss and write the Report for Prac 3.
Safety
Not much to wo
y about with this lab – just don’t do anything stupid.
Equipment
Trifilar rig, Ruler, Stopwatch, 3 bolts, object, scales, Calculator, Brain
Tasks (in class)
1 Measure the natural frequency of the empty Trifilar rig (the whole group)
1.a Practice setting the bare disk into torsional (twisting) vi
ations. Take care that the disk rotates with minimum swaying from side to side.
1.b Using the stopwatch provided, measure the natural frequency of torsional oscillations of the bare disk suspended by the three filaments. Repeat the experiment five times to determine the scatter in results.
1.c Enter your results into first row table 1 (at end of this sheet).
2 Calculate the radius of gyration and moment of inertia of the Trifilar rig from the natural frequency (the whole group)
2.a The equation for the natural frequency of torsional oscillation is:
f
n
=
1
2
p
g
2
k
2
L
Hz
where fn is the natural frequency of torsional vi
ations, r is the radius of the pitch circle on which the filaments are fixed to the disk, k is the radius of gyration of the disk, and L is the length of a filament. If you want to see how it is derived see Appendix 1.
2.b Rea
ange the formula in section 2.a to allow you to calculate the radius of gyration from the natural frequency.
2.c Calculate the moment of inertia of the empty disk from the radius of gyration.
2.d Enter your results into first row of table 1.
3 Calculate the radius of gyration and moment of inertia of the Trifilar rig with different a
angements of bolts/object (from the natural frequency)
3.a Repeat steps 1 and 2 to determine the radius of gyration and moment of inertia for the Trifilar rig with:
· An object in the centre of the disk. (member A of the group)
· Three bolts to the inner set of holes (nothing in the centre hole). (member B of the group)
· Three bolts to the middle set of holes (nothing in the centre hole). (member C of the group)
· Three bots to the outer set of holes (nothing in the centre hole). (member D of the group)
3.b Enter your results into the appropriate rows of table 1.
4 Measure and Weigh
4.a Make sure that you have filled out all the data in table 2 so you can finish the calculations out of class
Report Guideline:
Requirement
Weighting (%)
Attendance
Conduction the experiment (Coversheet included
with names of other team members)
5
Introduction
Introduction and scope
10
Results 1
List your results from the practical. What times you recorded, and the number of oscillations. List any assumptions you have made, and include a diagram of your setup
10
Calculations 1
Clearly fill in table 1 and 2 in the practical sheet, include these in your report (hand written will not receive full marks)
10
Calculations 2
Show sample calculations of each of the shaded cells, state assumptions you made for these calculations
20
Discussion 1
Comment on the difference between the experimental and theoretical results (if any) and what caused it?
10
Discussion 2
What would the percentage e
or have been if you compared moment of inertia instead of radius of gyration? Comment on reasons why.
10
Discussion 3
Was agreement between the experimental and theoretical results enough to give you confidence in using the rig to find moment of inertia? Explain your reasoning
10
Conclusion
Conclusion
ecommendation
10
Grammar and references
References, grammar…
5
Marking Ru
ic
0%
25%
50%
75%
100%
Attendance
Student did not attend the practical
NA
Student attended the practical and did not attach a coversheet with list of group members
NA
Student attended the practical and attached a coversheet with list of group members
Introduction
Student provided no introduction or scope
Student neglects to provide either an introduction, or a scope in the report
Student provided a
ief introduction and scope of the practical report.
Student provides an introduction and scope that outlines the practical and its relevance
Student provided a comprehensive (not necessarily big) introduction explaining the relevance of the practical, and applications of the ideas discussed. Scope is well constrained and outlines the required deliverables
Results 1
Student did not (or inco
ectly) provide any practical results
Student did not provide all measured practical results in tabular form
Student summarised recorded practical data in tabular form in SI units
Student summarised recorded practical data in tabular form in SI units with co
ect formatting, assumptions listed for recording data and calculations
Student summarised data in tabular form with all practical results in SI units, co
ect formatting in a logical, easy to read manner with no e
ors, and a co
ectly labelled diagram
Calculations 1
Student does not include tables
Student includes tables, but they are incomplete, or hand written
Student includes tables
Student includes tables, in SI units, with units shown in co
ect format
Student includes tables, in SI units, with units shown in co
ect format, in a logical, easy to read way
Calculations 2
Student does not show calculations
Student shows calculations, but they are inco
ect or incomplete
Student shows basic sample calculations
Student shows calculations, listing symbols used
Student shows calculations, listing symbols used, and states any assumptions made during the calculations
Discussion 1
Student does not answer the question
Student comments on differences but does not discuss reasoning
Student comments on differences and
iefly discusses reasons
Student tabulates the differences in the results and presents a compelling argument for variations between the results.
Student tabulates the differences in the results, with co
ect formatting, and presents a compelling argument for variations between the results.
Discussion 2
Student does not answer the question
Student inco
ectly compares or calculates e
or percentage, does not list reasons for differences
Student co
ectly calculates percentage e
or of the two,
iefly comments on reasons for differences (if any)
Student co
ectly calculates percentage in e
or, tabulates and compares the data, provides reasoning for any differences
Student co
ectly calculates percentage in e
or, tabulates and compares the data with co
ect formatting, provides reasoning for any differences
Discussion 3
Student does not answer the question
Student provides an opinion, but does not explain reasoning
Student states whether they had confidence in their ability. Briefly explains reasoning
Student states whether they had confidence in their ability. Compares differences between the results, and explains reasoning for any differences
Student states whether they had confidence in their ability. Compares differences between the results in a co
ectly formatted table, and explains reasoning for any differences
Conclusion
Student does not write a conclusion or recommendation
Student does not clearly conclude the report, provides little to no recommendation on changes or improvements to the practical
Student writes a
ief conclusion of the report, and recommendations for changes or improvements to the practical
Student writes a succinct conclusion comparing and referencing results, does not introduce any new information, recommends any changes or improvements to the practical and some reasoning
Student writes a succinct conclusion comparing and referencing results in tabular form, does not introduce any new information, recommends any changes or improvements and reasoning behind their opinion
Grammar and references
Numerous spelling and grammar mistakes, no references for objectivity or others work
Many spelling and grammar mistakes, some sources are used
Some sources are used for objectivity, some grammatical e
ors
General acknowledgement of resources, no grammar e
ors
Sources fully identified, referenced co
ectly, connected with ideas, and no grammar e
ors
Appendix 1: Development of Trifilar equation
[(Fy = mag]
3
T
cos(
y
)
-
mg
=
ma
g
Neglecting vertical accelerations in comparison with other motions and assuming the small angle approximation gives:
3
T
-
mg
=
0
(A1.1)
[(My = Iy(]
q
y
&
&
y
I
T
-
=
)
sin(
3
Noting that from geometry, for small values of (:
sin(
y
)
»
q
L
gives:
q
q
&
&
y
I
L
T
-
=
2
3
o
0
3
2
=
+
L
T
I
y
q
q
&
&
Noting from equation A1.1 that 3T=mg gives:
0
2
=
+
L
mg
I
y
q
q
&
&
which is the classic equation for undamped vi
ations with the standard mathematical solution:
q
=
q
0
sin(
w
n
t
)
with circular natural frequency given by:
w
n
=
mg
2
I
y
L
(A1.2)
Noting that n = 2fn and Iy = mk2 (k = radius of gyration) gives:
f
n
=
1
2
p
g
2
k
2
L
(A1.3)
For comparison purposes, rewriting this as:
f
n
=
1
2
p
k
g
L
shows that it is similar in form to the equation for free vi
ation of a simple pendulum (
f
n
=
1
2
p
g
L
)
Appendix 2 Guide to calculating radius of gyration from a trifilar test
When finding the radius of gyration of an unknown object in this trifilar test, there are two components to the rotating inertia:
1. The disk (platform)
2. The test object
You can’t add radii of gyration, but you can add moments of inertia. So (remembering that I = mk2) what you must do is modify equation A1.3 as follows:
f
n
=
1
2
p
mg
2
(
I
yplatform
+
I
yobject
)
L
You can get Iy platform from your test value for its radius of gyration and the given value of mass, so you can find Iy object and hence find the required radius of gyration.
Table 1
NOTE: shaded cells can be calculated after class for the report
Setup No:
______
Object:
______
Natural frequency (raw)
Natural frequency (repeatability/ range)
Natural frequency (average)
Experimental
Theory