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The determination of the moment of inertia of a flywheel is a crucial aspect of engineering, particularly in the design of engines and machinery. The moment of inertia is a measure of an object's resistance to changes in its rotational motion. In the context of a flywheel, it plays a significant role in maintaining the stability and efficiency of various mechanical systems, such as piston-driven engines.
The primary objective of this experiment is to find the moment of inertia of a flywheel and then compare it with the theoretical value.
This comparison allows us to assess the accuracy of our measurements and calculations, ultimately leading to the identification of any percentage error in our readings. Understanding the moment of inertia of a flywheel is essential because it influences the selection of an appropriate flywheel to ensure the smooth and efficient functioning of pistons and other mechanical components.
The following apparatus and materials were used for this experiment:
Flywheel:
A flywheel is a mechanical device designed to efficiently store rotational energy and resist any changes in rotational energy due to its large moment of inertia.
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In the context of an engine, a flywheel plays a crucial role in the smooth movement of a piston. During the engine cycle, there is only one power stroke (Expansion stroke), and in all other strokes, power must be supplied for piston movement, which comes from the flywheel. The flywheel stores energy from the power stroke in the form of rotational kinetic energy and releases this energy to drive the piston during other strokes.
Thus, a flywheel provides continuous power output in situations where the energy source is not continuous.
There are two main types of flywheels:
Moment of Inertia:
Moment of inertia is a property of a body that resists changes in its rotational movement when subjected to an external force like torque. It is specified using an axis whose position is not fixed and is a measure of the body's resistance to angular acceleration. Moment of inertia is an additive property, and it can be calculated for bodies with specific shapes using integral calculus.
The flywheel apparatus used in this experiment was properly lubricated to minimize frictional errors. The height of the string was set to be equal to the length of the string. The string was tightly wound around the axle of the flywheel. A mass 'm' was attached to the free end of the string. When this mass falls, it unwinds the string and sets the flywheel into rotational motion. The flywheel continues to rotate due to its rotational inertia but eventually comes to rest due to frictional forces.
The theoretical value of the moment of inertia is given by: I = Mr2
Given data:
| Reading No. | Falling mass M (lb) | Time (sec) | Average Time (sec) | ||
|---|---|---|---|---|---|
| Lb. | t1 | t2 | t3 | ||
| 1 | 0.75 | 42 | 40 | 41 | 41 |
| 2 | 1.25 | 28.6 | 28.6 | 28 | 28.6 |
| 3 | 1.75 | 25.1 | 25.1 | 25 | 25.1 |
Calculations:
| Reading No. | Falling mass M (lb) | Linear acceleration (inches/s2) | α1 (spindle) | α2 (wheel) | Tension (lb·inches)/s2 | τ1 (spindle) | τ2 (wheel) | lb·inches2 |
|---|---|---|---|---|---|---|---|---|
| Lb. | ||||||||
| 1 | 0.75 | 0.054 | 0.108 | 8.05 | 289 | 144.5 | 1936.3 | 17923 |
| 2 | 1.25 | 0.111 | 0.222 | 16.5 | 482.2 | 241.1 | 3230.74 | 13567 |
| 3 | 1.75 | 0.145 | 0.29 | 21.6 | 676 | 338 | 4529.2 | 14560 |
Mean value of the moment of inertia of the flywheel = 15351 lb·inches2 = 0.6 kg·m2
Theoretical value of the moment of inertia of the flywheel = 0.8 kg·m2
Total percentage error in this experiment = 25%
The observed percentage error in this experiment raises important considerations. Several factors could contribute to the deviation between the experimental and theoretical values of the moment of inertia. One potential source of error is the measurement of time, which could be influenced by human reaction time and stopwatch accuracy. Additionally, the height and length measurements may have introduced inaccuracies.
Another factor to consider is frictional forces experienced by the flywheel during its rotation. Friction can lead to energy losses, which may not have been accounted for in our calculations. Additionally, variations in the flywheel's behavior due to factors like air resistance and imperfections in the apparatus could contribute to the observed error.
This experiment aimed to determine the moment of inertia of a flywheel and compare it to the theoretical value. While the mean experimental value of moment of inertia was found to be 0.6 kg·m2, the theoretical value was 0.8 kg·m2, resulting in a total percentage error of 25%. This discrepancy suggests that there were inaccuracies in our measurements and assumptions.
Potential sources of error include measurement precision, frictional losses, and variations in the behavior of the flywheel. To improve the accuracy of future experiments, more precise measurement tools and techniques should be employed. Additionally, efforts to minimize friction and control external factors that affect the flywheel's motion should be considered.
Despite the observed error, this experiment provides valuable insights into the practical challenges of measuring moment of inertia and highlights the importance of considering various factors in engineering applications.
Flywheel Moment of Inertia Lab Report. (2024, Jan 04). Retrieved from https://studymoose.com/document/flywheel-moment-of-inertia-lab-report
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