Measuring the Moment of Inertia of a Flywheel


Length: 740 words (2.1 double-spaced pages)
Rating: Excellent
Open Document
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Text Preview

More ↓

Continue reading...

Open Document

Measuring the Moment of Inertia of a Flywheel



Objective
=========

Measure the angular velocity of a flywheel and use conservation of
energy to calculate its moment of inertia.



Apparatus
=========

Flywheel

String

Slotted mass on hanger

Stop-watch

Vernier caliper

Metre ruler



Theory
======

The rotational kinetic energy can be defined by the equation K=1/2 I ω2.
Where I is the moment of inertia of the body about the axis of
rotation.

In this experiment, the flywheel rotates freely about a horizontal
axis. The radius of the axle of the flywheel can be measured with a
caliper. As m falls, its gravitational potential energy is transferred
into translational kinetic energy of m, rotational kinetic energy of
the flywheel and work done by friction. As the flywheel completes N
further turns, its original rotational kinetic energy is transferred
into friction loss. Assume the flywheel decelerates uniformly. Thus,
the moment of inertia of the flywheel can be determined.



Procedure
=========

1. The flywheel was set as shown with the axle of the flywheel
horizontal. A polystyrene tile was placed on the floor to avoid the
impact of the mass on the floor.

2. The vernier caliper was used to measure the diameter d of the axle.
The mean of two perpendicular measurements was taken.

3. The hanger with appropriate amount of slotted mass was put on the
tile. Use the balance to measure the total mass m.

4. Sufficient length of string was attached to the hanger so that the
free end wraps once round the axle of the flywheel.

5. The mass was winded up to an appropriate height.

6. Verified that the string fell off the axle when the mass hit the
ground. A label was put on the curved surface of the flywheel. The
mass was winded up again.

7. The height h of the mass was measured. The height h was recorded.
The number of revolutions n1 that the flywheel made was calculated as

How to Cite this Page

MLA Citation:
"Measuring the Moment of Inertia of a Flywheel." 123HelpMe.com. 27 May 2017
    <http://www.123HelpMe.com/view.asp?id=149828>.
Title Length Color Rating  
This Is The Moment Essay - This IS the moment This war-torn land shows nothing but death and the dying. The ground is muddy from the rain, which also makes the ground wet. Up above the trench line is barbed wire and … nothing else. No birds, no animals … no people. A few dead bodies of the brave men going to assassinate the enemy by night fall. No. No one makes it. Never. There’s the constant gun bangs and the sound of explosions from the grenades. The sky is lit up by the flashes of guns against the silver clouded sky. Nobody dares to look up for more than a few seconds otherwise the enemy sharpshooters will get them....   [tags: Personal Experience, Autobiography] 757 words
(2.2 pages)
Good Essays [preview]
Transformation and Inertia Essay - Transformation and inertia are presented as conflicting forces, balanced against one another in a kind of universal tension. The individual changes biologically as well as intellectually and spiritually, but his physical progression from youth to old age follows a path more or less set by nature. Nature itself changes cyclically, but the cycle of the seasons—the cycle of life—is repeated over and over. The classics of literature possess permanence in their expression of universal meaning, their relevance to men in all times....   [tags: conflicting forces] 336 words
(1 pages)
Strong Essays [preview]
In the Moment Essay - "Time is an absurdity, an abstraction. The only thing that matters is the moment." (Nolan 12). If this is true, then in the story "Memento Mori" and the movie Memento, it is ironic how the main character, Leonard, who is suffering from severe memory loss, is constantly trying to figure out the past, even though he knows he will not remember it once he learns what has happened. His wife is dead, and he is searching through a system of notes and Polaroid pictures for her killer. Though the story is unclear at first, through narration, structure, and repetition, the plot of the story becomes clearer....   [tags: American Literature] 613 words
(1.8 pages)
Good Essays [preview]
Inertia Essays - Centuries of thought and experimentation by several of the greatest minds to ever walk the earth have contributed to the awareness of this property of matter known as Inertia. It all began with the investigation of an ancient Greek scientist and philosopher by the name of Aristotle. Through countless observations and hypotheses, Aristotle grew almost certain of a few things involving motion. Aristotle’s findings suggested mainly that Earthly objects seek their natural place at rest. This natural place related to earth, water, air and fire respectably....   [tags: essays research papers] 545 words
(1.6 pages)
Strong Essays [preview]
A Defining Moment Essay - Many people influenced and events my reading and writing development throughout my childhood from my mother, my elementary librarian, and Sesame Street, to getting my first pair of glasses. We all have defining moments in our lives where we can look back and say, “That moment changed my life.” This is the story of the defining moment that changed the way I read and write, and I learned it from a whale. It was the beginning of my seventh grade year. I was about twelve years old and, I guess you could say a nerd....   [tags: Personal Narrative, Personal Experience] 751 words
(2.1 pages)
Good Essays [preview]
A Moment of Innocence Essay - A Moment of Innocence When I walked into class that day I was indifferent to the movie that we would be watching that evening. Five minutes into A Moment of Innocence (1995) by Mohsan Makhmalbaf, I was hooked. By taking a pseudo-documentary style Makhmalbaf lets us see the people as they are transformed into the characters from the director’s past. This style allows us to “grow up” with them and to relate to both sides of the story. By taking a true event and fictionalizing, at least part of it, Makhmalbaf has us trying to figure out what parts have been added to the narrative and which parts truly speak to history....   [tags: essays papers] 1145 words
(3.3 pages)
Strong Essays [preview]
Infinity in a Moment Essay - Infinity in a Moment Dear Mel, I’ve finally come to a conclusion…the first in my life I think. I’m in love. What an annoying nothing…the word love. Undermined after years of unrepresented use and manipulative thought. Contemporary teens, playing with matches to start a fire that will only burn down their own foundations of security and ontology. It’s a card trick to them, after all they’re immortal, apprehensions are as pointless as relationships. Throwing around promises that should tear the doors of heaven apart revealing metaphors incapable of description, but instead suffocates in a beer glass....   [tags: English Literature Essays] 922 words
(2.6 pages)
Strong Essays [preview]
Courageous Moment Essay - ... I started to see ramps everywhere I went, and imagined racing down them and jumping into the air magnificently. I also found myself getting distracted in class because I was daydreaming about completing the most epic of leaps. However, I was still crippled by fear when I contemplated actually reattempting this stunt since it had ended so disastrously the first time. I eventually built up my confidence and told myself that I simply must go back, and try successfully perform this trick successfully at least once....   [tags: skateboarding, achievement, tricks] 650 words
(1.9 pages)
Better Essays [preview]
Moment In Life Essay - Moment In Life I was born on 6 September 1980 in Bangkok, Thailand. The first two people that can describe me the best are my father and my mother. They told me that the first time they saw me they had the happiest time in their lives because I am the first son of them. They said that I was a curious and mischievous boy. When I was six years old, I entered Chulalongkorn University Demonstration school. In this school I was taught to be polite, responsible and loved in learning. I have made many friends in this school and I have had many experiences in this school, too....   [tags: essays papers] 542 words
(1.5 pages)
Strong Essays [preview]
Essay on a memorable moment - On April 17th, 2004, my eldest sister went into labor around 5:30 A.M. I honestly wasn't in the mood to go to the hospital so early in the morning, but my mother told me I should. My mom told me that it was a time when my sister really needed us. All I thought about was that she wouldn't even know whether I was there or not. My family and I took her to the hospital, and then everyone waited in the adjacent room. I never thought much about it, so I fell asleep. To me it was like," Whatever," she's just having a baby, another niece or nephew for me....   [tags: essays research papers] 479 words
(1.4 pages)
Strong Essays [preview]

Related Searches




the mass was wound up.

8. The mass was released and at the same time the stop-watch was
started.

9. As soon as the mass hit the ground, timing was stopped and the
number of revolution n2 that the flywheel performed was counted before
it came to rest.

10. The mass was winded up again and steps 7 to 9 were repeated for at
least 3 times. The mean values of the falling time t and n2 were
obtained.



Precautions
===========

1. The mass and the height from which the mass falls should be chosen
so that the falling time is long enough for measurement to be taken
accurately. The mass and the height should not be changed throughout
the experiment once they have been chosen.

2. The first few turns of the string should overlap the others.

3. The mass should be wound up to the same height in all trials.

4. When using the stop-watch, the hand should be held straightly to
minimum the reaction time error.

5. Do not stand too close to the polystyrene tile when releasing the
mass.

6. When choosing the appropriate amount of the slotted mass, a smaller
amount (e.g. 1 slotted mass) should be chose to try first.

7. The later turns of the string should not overlap the others.



Result and calculation
======================

Mass m = 0.2 kg

Height h = 0.80 m

Axle diameter d = 0.0522 m

→ radius r = 0.0261 m

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

mean

Time t/s

1.75

1.85

1.84

1.84

1.81

1.78

1.82

1.78

1.81

No. of revs n1

5

5

5

5

5

5

5

5

5

No. of revs n2

25

27

23

26

26

24

25

23

25

Suppose v is the final velocity of the mass when it reaches the floor
and ω is the angular velocity of the flywheel at this instant. Then

v = 2 × average velocity during fall = 2h / t

= 2 × 0.8 ÷ 1.81

= 0.88 m s-1

ω = v / r

= 0.88 ÷ 0.0261

= 33.9 rad s-1

From the conservation of energy,

Decrease in Increase
in Work done

gravitational potential = kinetic
energy + against

energy of falling mass of mass and
flywheel friction

i.e. mgh = 1/2 mv2 + 1/2 Iω2 + n1W

where W is the work done against friction per revolution.

Since the kinetic energy acquired by the flywheel ( 1/2 Iω2) is
dissipated in n2 revolutions,

n2W = 1/2 Iω2

W = Iω2 / 2n2

Substituting,

mgh = 1/2 mv2 + 1/2 Iω2 + n1W

mgh = 1/2 mv2 + 1/2 Iω2 + n1Iω2 / 2n2

I = mr2 ( n2 / n1 + n2 ) ( gt2 / 2h – 1)

=0.2 × (0.0261)2 ( 25 / (25 + 5) ) ( 10 × (1.81)2 / 2 × 0.8 – 1 )

=2.21 × 10-3 kg m2



Conclusion
==========

The moment of inertia of the flywheel is measured and found to be 2.21
× 10-3 kg m2.



Discussion
==========

Errors and improvement

1. The reaction times error. This can be improved by straighten the
hand when taking the time.

2. The number of revolution n2 that the flywheel performed cannot be
accurately obtained. This can be improved by counting the number of
revolution by two students instant of one and to repeat the experiment
more times.

3. Unsteady hands. When the hand released the mass, force may be push
to the mass. To improve this, student should release the mass slowly
and softly.



Reference
=========

Physic Beyond 2000


Return to 123HelpMe.com