# Measuring the Moment of Inertia of a Flywheel

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

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

#### Text Preview

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 Ï‰2.
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

## Need Writing Help?

Get feedback on grammar, clarity, concision and logic instantly.

MLA Citation:
"Measuring the Moment of Inertia of a Flywheel." 123HelpMe.com. 22 May 2018
<http://www.123HelpMe.com/view.asp?id=149828>.
Title Length Color Rating
- ... After finding the angular acceleration, the experimental moment of inertia was calculated for all the trials by using equation 1 below. I_experimental=(mr_p (g-r_p α))/α (1) In the equation above, Iexperimental¬ is the experimental moment of inertia, m is the mass of the hangar and the added masses, r_p is the radius of the 3-step pulley, and α is the angular acceleration. The experimental moment of inertia calculated using the angular acceleration with the ring was the experimental moment of inertia for the entire system; therefore, the moment of inertia of the ring must be calculated....   [tags: analysis, experiment, laboratory] 785 words
(2.2 pages)
Better Essays
- 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
- My right hand moves with fluidity and precision; my left holds steady the drafting paper and journeys to my desk to retrieve items integral to the task: the ruler, compass, eraser, and my coffee mug. All the while, my mind hums along, scrutinizing every detail. The repetitive nature of this work used to calm me, especially when I was younger and the stakes were lower. Back then, my creations were little more than the product of an overactive imagination, designed to make life easier or more comfortable....   [tags: personal narrative] 1295 words
(3.7 pages)
Powerful Essays
- Cursing as the last of the embers slowly died out, he stuffed his pipe into the logs to light the herb. Content, he took a long drag, leaning back on his elbows, inhaling the salty smell of the quietly splashing waves which had a surprisingly calming effect on him. “I thought you gave up that horrendous habit,” drawled an unmistakable voice. He looked up. She was feet away from him, yet hidden in the shadows. Her long, white dress and loose stands of hair billowing in the cool breeze. Her ring still glints at her finger, yet she removes it and tosses it into the sand to bury as soon as she realises its presence....   [tags: A Short Story] 560 words
(1.6 pages)
Good Essays
- "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
- 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
- Angular momentum is the relationship between Rotational Inertia and Rotational Speed. More simply, it is the tendency an object has to continue moving in a circle or spinning. Angular Momentum = Angular Velocity x Rotational Inertia When a figure skater pulls their arms closer to their body, they are reducing their Rotational Inertia, making themselves more aerodynamic. In order to sustain this and maintain their momentum, the Rotational Speed must increase. Angular Conservation Angular momentum is basically an object’s resistance to a change in rotation....   [tags: Inertia, Physics, Momentum] 602 words
(1.7 pages)
Good 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
- Measuring The Rate Of Osmosis In Potato Cells Skill Area P. Osmosis is defined as free water molecules diffusing from a high concentration to a low concentration through a semi-permeable membrane. Variables - The rate of osmosis effected by many different living things, temperature of the solutions, surface area over which it can occur, Volume of solution, Volume of potato, distance through which the free water molecules have to pass and finally the difference in concentration of the solutions....   [tags: Papers] 1995 words
(5.7 pages)
Strong Essays
- 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

### 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

â†’ 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 Ï‰ is the angular velocity of the flywheel at this instant. Then

v = 2 Ã— average velocity during fall = 2h / t

= 2 Ã— 0.8 Ã· 1.81

= 0.88 m s-1

Ï‰ = v / r

= 0.88 Ã· 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 IÏ‰2 + n1W

where W is the work done against friction per revolution.

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

n2W = 1/2 IÏ‰2

W = IÏ‰2 / 2n2

Substituting,

mgh = 1/2 mv2 + 1/2 IÏ‰2 + n1W

mgh = 1/2 mv2 + 1/2 IÏ‰2 + n1IÏ‰2 / 2n2

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

=0.2 Ã— (0.0261)2 ( 25 / (25 + 5) ) ( 10 Ã— (1.81)2 / 2 Ã— 0.8 Â– 1 )

=2.21 Ã— 10-3 kg m2

Conclusion
==========

The moment of inertia of the flywheel is measured and found to be 2.21
Ã— 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