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Unformatted text preview: PHY 122: Lab: Rotational Motion Name: Thomas Andrews Group members’ names: Shannon Mendovich, Patrick Champagne,
Trevor Baldwin Group number: 1
Class Number: 13726 Day and Time: Monday, 8:00 AM Objective: The objective of this lab is to look at rotational motion from an energy viewpoint. This is done
by a constant torque that will create a constant angular acceleration. Another objective will also be top show that the moment of inertia depends on the rotation axis for a given oject. Experimental Data: Mass of block: 0.432kg
Mass of hanging mass: 0.02j g rs = 0.0048m
rm = 0.0143m
Table 1: Short Axis
Small Long Axis Long Axis
9.47 rad/s2 27.4 rad/s2
107.88 rad 35.90 rad 43.81 rad/s 41.89 rad/s Short Axis
19.9 rad/s2
17.9 rad 27.4 rad/s Data analysis: Calculations for short axis with small pulley: Static Moment of Inertia:
1 Is = 1—2M(a2 + b2) 1
IS = 1—20.432(0.0492 + 0.042) IS = 1.44 * 10‘4Kgm2
Error Analysis: A, — (“SA )2+(0’slb)2+(a’sl )2
5— 0a a. 6b ' 6m m 2 1 2 1 2 1
_ _ _ 2 2
(IZmZaAa) +(12m2bAb) +(12(a +b )Am) AIS 2 Al — (i (0 432)(2) (0 049)(0 00005))2 + (i (0 432) (2) 0 04)(0 00005))2 + (—1( 0492 + 042)(0 001))
s — 12  . . . 12 . ( . . 12 . . . AIS = 4.03 * 107 Dynamic Moment of Inertia: g — TC!)
0!
9.8 — ((0.0048)(6.26))
6.26 Id = 3.2 * 10‘3kgm2 Id=mr( 1d = (0.432)(o.0048)( Error Propagation: 61d
Ald = 'a—a‘aa Ala = V ((mgra—2)(Aa))2
AId = J (((0.432)(9.8)(0.0048)(6.26)‘2)(0.017))2 AId = 1.71 * 10—5 Calculations for small pulley with medium Pulley: Static Moment of Inertia:
1
= _ 2 2
IS 12M(a + b )
1 2 2
Is = EO.4BZ(0.049 + 0.04 )
IS = 1.44 * 10—41(ng Error Analysis: A, — (51s,. )2+(6’sib)2+(a'si )2
5— aa a 6b 6m m 2 2 2 1 1 1 2 2
A15: (1—2m2aAa) +(ﬁm2bAb) +(ﬁ(a +b )Am) ? 2 AI — (1(0 432)(2) o 049 0 00005 )2 + (i (0 432)(2)(0 04)(0 00005)) + (i( 0492 + 042)(0 001))
5 _ 12 ' ( ' )( ' ) 12  . . 12 _ _ . AIS = 4.03 * 107 Dynamic Moment of Inertia: g — ra
a ) 9.8 — ((0.0143)(19.9) _19.9 ) Id = 2.9 * 10'3kgm2 Id=mr( 1d = (0.432)(0.0143)( Error Propagation: 01d
Ald = '6; 6a Nd = a} ((mgra—2)(Aa))2
Nd = 1/(((0.432)(9.8)(0.0143)(19.9)‘2)(0.35))2 Ald = 5.35 * 10‘5
Calculations for Long Axis and Small Pulley: Static Moment of Inertia: 1
Is = 1—2M(a2 + b2) 1
IS = 1—20.432(0.042 + 0.032) Is = 9.0 * 10‘5Kgm2 Error Analysis:
A, _ (“SA )2+(015Ab)2+(01si )2
5‘ aa “ 00 am m
1 2 1 2 1 2
= — — _ 2 2
AIS (lZmZaAa) +(12m2bAb) +(12(a +b )Am) 2 2 2 A15 (—11—2'(0.432)(2)(0.04)(0.00005))‘ + (é(0.432)(2)(0.03)(0.0‘0005)) +( —1~—( 042 + 032)(0 001))
12 . . . AIS = 2.08 * 10'4 Dynamic Moment of Inertia: g — m:
a I
9.8 — ((0.0048)(9.47)
9.47 ) Id = 2.1 * 10‘3kgm2 Id=mr( 1d = (0.432)(0.0048)( Error Propagation: Na = 1/ ((mgra‘zXAaDz
Ald = J(((0.432)(9.8)(0.0048)(9.47)—2)(0.033))2 Aid = 7.74 * 10—S Calculations for Long Axis Medium Pulley: Static Moment of Inertia: 1
__ 2 2
15—12M(a +b) 1
IS = 130.432(0.042 + 0.032) IS = 9.0 * 10—51(ng Error Analysis:
615 2 615 2 615 2
“s— (ea—a“) WW”) Wham")
1 2 1 2 1 2
= — _ _ 2 2
AIS (lZmZaAa) +(12m2bAb) +(12 (a +b )Am) 2 2 2 1 1 1
A15 (E(0.432)(2)(o.04)(0.00005)) +(E(0.432)(2)(o.03)(o.00005)) +(1—2—(.042 +.032)(o.oo1)) AIS = 2.08 * 104 Dynamic Moment of Inertia: g—ra
a ) 9.8 — ((0.0143)(27.4)
27.4 ) Id = 2.1 * 10‘3kgm2 Id=mr( I, = (0.432)(0.0143)( Error Propagation: 01d
AId = “£66! Nd = x! ((mgra—ZXACZDZ
A1,, = w/(((0.432)(9.8)(0.0143)(27.11.)2)(0.011))2 A1,, = 8.87 * 10—7 Results: Short Axis Long Axis
1.44 * 10—41(ng 9.0 * 10—51(ng
i403 * 10‘7 Kng i208 * 10'4 1(ng Long Axis, Long Axis,
Small Pulley Medium Pulley 2.1 * 10—3kgm2 i774 * 10'5 Kgm2 i887 * 10'5 1(ng Discussion and Conclusion: Overall, the objective of this lab was to show that the moment of inertia depends on the
axis of rotation. Also, to look at rotational motion from an energy point of View. The moment of
inertia is deﬁned as the difficulty for an object to rotate. There are two types of moment of
inertia, Dynamic and Static. These will be calculated through the following experiments. To test this concept, there were four experiments. All of these experiments changed the pulley and the axis of rotation. The ﬁrst experiment was a short axis with a small pulley. The
second was a medium pulley and a short axis of rotation. The third was a long axis of rotation
and a small pulley. The last experiment was a long axis of rotation and a medium pulley. All of
these experiments were performed in the same way. The mass was placed on the axis and another
mass was wrapped around a pulley. Then, the mass will pull the other mass causing the mass to
rotate. That is how the moment of inertia is calculated. At the end, all of the moment of inertia
and angular velocities were calculated. The results of this lab showed that the moment of inertia does depend on the axis of
rotation. The results for the short axis and small pulley are 3.2 * 10‘3kgm2. This was for the
dynamic moment of inertia. The static moment of inertia was 1.44 * 10‘4Kgm2. As the results
show, There is a difference between the static and dynamic moment of inertia. This stayed true
for the rest of the four experiments. Although there were some errors in the experiments. Some
systematical error could be the friction of the pulley and the friction between the pulley and the
string. Also, there could be error in the weight of the mass and the weight of the string was not
accounted for. There could also be statistical errors. The angular velocity could have statistical
error because it was calculated from a line of best fit. This is a statistical error because the line of
best fit is not an accurate measurement. Overall, there were some errors in the lab, but the main
objectives were achieved. In the end, the theory that the moment of inertia depends on the axis of rotation was conﬁrmed. Rotational Motion.ds 04/10/2017 09:03 AM
Graph 1 . r" I I" . I."
_ x _l.
01
O 8
o Angular Position( rad )
01
O O .h
0 O 'ty'grad/s 2))"
o m ( Slope) 9.47 :t 0.033 b ( Y Intercept) 1.52 :t 0.096
r 1.00
Mean Squared Error 0.127
Root MSE 0.356 Angular [elem
O Rotational Motion.ds 04/10/2017 09:00 AM
Graph 1 _ L
d
01
o O
O 50_ Angular Position( rad ) I
”woo
01001 0 IV
01 o m (Siope) 6.37 :t 0.017 D (Y Intercept) 5.70 :r: 0.067
r 1.00
Mean Squared Error 0.0432
Root MSE 0.208 O Angular Velocitﬂ rad/s )
o 01 _ Rotational Motion.ds 04/10/2017 09:02 AM
Graph 1 a)
O u:
C Angular Posiﬁon( rad ) C
B 3 0 30 25
‘20
(I)
E15 m (Slope) 19.8:t0.35
: b ( Y Intercept) 9.08 :I: 0.45
€10 r 0.996
0 Mean Squared Error 0.472 Root MSE 0.687 0'! Angular Vel Rotational Motion.ds 04/10/2017 09:04 AM
Graph 1 140
120 ' Angular Position( rad _)_ 3
h~ N A 0') oo o
o o o O o O O O m ( Slope) 27.4 :t 0.11 b (Y Intercept) 14.5 :l: 0.15
r 1.00
Mean Squared Error 0.0405
Root MSE 0.201 Angular_\_/elocity( rad/s 2° *
o 3 ...
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