Experiment-4 Mass Moment of Inertia - Copy

7/24/2019 Experiment-4 Mass Moment of Inertia - Copy

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Experiment 4: Mass Moment of Inertia I

Experimental Mass Moment of Inertia Part A

Equipment:Model LS-2108, a stopwatch, a weihin scale, a meas!rin tape, and "

lenths of steel wire#

Objectives:1# $he experiment is to determine experimentall% the moment of

inertia and radi!s of %ration of a rectan!lar &ar#

2# 'omparison &etween experimental and theoretical res!lts#

Experimental procedure:

1# $he (al!es of lenth of rope, L, centre distance, r, mass ofrectan!lar &ar, M, and the dimensions of &ar a, &, and l are

o&tained and meas!red#

2# $he &ar is connected with e%e &olts with nelii&le mass onto the

wires with the clips pro(ided#

"# $he &ar is twisted hori)ontall% to p!t it into oscillation a&o!t its

(ertical axis to a simple harmonic motion#

4# $he &ar is left !ntil it oscillates in a stead% state#

*# $he time is o&tained in seconds ta+en for 20 oscillations#

# $he (al!e is di(ided with the n!m&er of oscillations to o&tain timeta+en for 1 oscillation# $he experiment is repeated to o&tain time

ta+en for "0, 40, *0, and 0 oscillations to o&tain a more precise

(al!e for the period in seconds#

# $he (al!e of the radi!s of %ration, ., and moment of inertia, I are

calc!lated !sin the followin e/!ation pro(ided#

t=2( IL

Mg r2 ) or t=2(

k2L

r2

g) for I=M k2


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ResultsMass of rectan!lar &ar: 1#+

Item Lengt !m"a 0#02*& 0#04l 0#202L 1#0r 0#0**

$a&le 4#1: imensions

$a&le 4#2: With afacing up,

Oscillation Period !s" #ime for $oscillation !s"

20 41 2#0*"0 2 2#040 82 2#0**0 10" 2#00 12* 2#08

Average time for $ oscillation !s" %&'(

$a&le 4#": ithb

facin !p,Oscillation Period !s" #ime for $

oscillation !s"20 42 2#1"0 " 2#140 84 2#1*0 10 2#120 12 2#12

Average time for $ oscillation !s" %&$$

)iscussions$heoretical (al!e for the moment of inertia of a rectan!lar &ar is,

I=M(a2+l2 )

12or I=

M(a2+b2 )12

With afacing up experimental calculation theoretical calculation * error


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t=2( IL

Mg r2 ) I=M(a

2+l

2 )12

I I=0.00558kg.m2 I=0.00552kg.m2 1#0

With afacing up

experimental calculation

K= I

M

theoretical calculation

K= I

M

* error

K K= 0.0591m2

K= 0.0587m2

0#8

With bfacing up


t=2

( IL

Mg r2 )


I=M(a2+l2 )

12 * error

I I=0.00585kg.m2

I=0.00565 kg.m2

"#*4

With bfacing up


K= I

M


K= I

M

* error

K K= 0.0605m2

K=0.0594 m2

1#8*

+onclusion$he experimental calc!lation for &oth radi!s of %ration 3. and

moment of inertia 3I were compared with theoretical (al!es o&tained

!sin the form!la pro(ided# $he error fo!nd in the experiment is less than

*5 in each case with a facin !p and & facin !p# $herefore the

experiment data is accepted# $he main reason for occ!rrence of error is

d!e to the h!man error that occ!r in the process of record the time withrespect to start and stoppin of stopwatch# In concl!sion it is pro(ed that

&oth the form!la we !sed in experimental and theoretical calc!lation is

accepted to !se#


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Experimental Mass Moment of Inertia Part ,

Equipment:

Model LS-2108, a stopwatch, a weihin scale, a meas!rin tape, and "



inertia and radi!s of %ration of a rin#



1# $he (al!es of lenth of rope, L, mean radi!s of rin, 6, o!ter radi!s

r1 , inner radi!s, r2 , and mass of rin, M are o&tained and

meas!red#2# $he rin is connected with e%e &olts with nelii&le mass onto the

wires with the clips pro(ided#"# $he rin is twisted hori)ontall% to p!t it into oscillation a&o!t its

(ertical axis to a simple harmonic motion#4# $he rin is left !ntil it oscillates in a stead% state#


# $he (al!e is di(ided with the n!m&er of oscillations to o&tain time

ta+en for 1 oscillation# $he experiment is repeated to o&tain time


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t=2 ( ILMg r2 ) or t=2(k2L

r2

g) for I=M k2

R=r1+r

2

2

ResultsMass of rectan!lar &ar: 1#+

Item Lengt !m"r1 0#08

r2 0#0*

l 0#024L 1#0

$a&le: 6in imensions


Oscillation Period !s" #ime for $

oscillation !s"20 41 2#0*"0 2 2#040 84 2#1*0 10* 2#10 12 2#1

Average time for $ oscillation !s" %&'-

)iscussions$heoretical (al!e for the moment of inertia of a rectan!lar &ar is,

I=l (r1

4r

2

4 )2

=mass per unit volume , r1=outer radius , r2=inner radius


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experimental calculation theoretical calculation * error

R=r1+r

2

2

67 0#08

v= r12

l r22

( 70.000246

m

3

=M

v

=7967.48 kg /m3

sin the form!la,

t=2

( IL

Mg r2

)and sol(in for I,

I=0.00974kg.m2

sin the form!la,

I=l (r1

4r

2

4 )

2

and sol(in for I,

I=0.00935 kg.m2

4#1


K= I

M


K= I

M

* error

K= 0.0705m2 K= 0.0691m2 2#0"






d!e to the h!man error that occ!r in the process of record the time withrespect to start and stoppin of stopwatch# In concl!sion it is pro(ed that


accepted to !se#


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Experimental Mass Moment of Inertia Part +

Equipment:Model LS-2108, a stopwatch, a weihin scale, a meas!rin tape, and "



inertia and radi!s of %ration of a c%linder#



1# $he (al!es of lenth of rope, L, center distance of c%linder, r, mass

of c%linder, M, lenth of c%linder, l, and radi!s of c%linder, 6, are

o&tain and meas!re#


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2# $he c%linder is connected with e%e &olts with nelii&le mass onto

the wires with the clips pro(ided#"# $he c%linder is twisted hori)ontall% to p!t it into oscillation a&o!t its

(ertical axis to a simple harmonic motion#4# $he c%linder is left !ntil it oscillates in a stead% state#


# $he (al!e is di(ided with the n!m&er of oscillations to o&tain time

ta+en for 1 oscillation# $he experiment is repeated to o&tain time





t=2

( IL

Mg r2

)or t=2

(k2L

r2

g)for I=M k

2

ResultsMass of rectan!lar &ar: 4#8 +

Item Lengt !m"R 0#0*

r 0#0*

l 0#0"L 1#0

$a&le: 6in imensions


Oscillation Period !s" #ime for $

oscillation !s"20 "4 1#"0 *1 1#40 8 1#*0 8 1#20 10" 1#2

Average time for $ oscillation !s" $&.$

)iscussionsTheoretical value for the moment of inertia of a rectangular bar is,


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I=M R

2

2

M = Mass of cylinder, R= radius of cylinder

experimental calculation theoretical calculation * error

sin the form!la,

t=2( IL

Mg r2 )

and sol(in for I,

I=0.0158 kg.m2

sin the form!la,

I=M R

2

2

and sol(in for I,

I=0.0151 kg.m2

4#4


K= I

M


K= I

M* error

K= 0.0576m2

K= 0.0563m2

2#"1






d!e to the h!man error that occ!r in the process of record the time with

respect to start and stoppin of stopwatch# In concl!sion it is pro(ed that


accepted to !se#

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Experiment-4 Mass Moment of Inertia - Copy