Rotational motion drew attention of the early scientists as human kind became fascinated by the night sky most specifically by the movement of the Moon, the Sun and the other objects which was termed as planti by the ancient Greeks and were later named planets. This interest was drawn in the ancient time in a practical nature. The Sun and the Moon were then used in the determination of the calendar as well as for navigation Berliner, L.J. and Reuben, J. eds., 2012. Galileo Galilei was one of the ancient scientists who made a pivotal contribution towards the development of the interest that was drawn to what is presently called the solar system.
Through his observations he proved the Copernican hypothesis as well as offering a foundation for accurate and reliable understanding of the movement of objects around the earth’s surface. Newton further developed on the ideas of Galileo to illustrate that the laws of motion that governed the heavenly bodies and those that were on earth were the same. Newton’s laws, especially the second law of motion which states that the rate of change of momentum of a body is directly proportional to the change producing it and takes place in the direction of the force fine-tuned the research. These two scientists offered the foundation of the study and exploration into rotational motion and its application in the synthesis of the astronomy Hadziioannou, C. et al 2012.
The reason of having interest in the topic rotational motion is its wide range of applicability in everyday life. Vehicles have to navigate sharp bends on various parts or sections of the road, it which in the worst case scenarios some have ended up toppling over as a result of errors from the drivers or an under or overestimation. Cycling a bike and navigating bending also applies the concept of rotational motion in which the motion of the wheels and making bends is associated with such concepts as angular momentum. This experiment will thus be an exploration of rotational motion by measuring the inertia moments of various distributions.
The motion of an object that is rigid and non-deformable is influenced by a combination of the rotation and the transition of the body. While the translation of the object defines its motion at its center, the rotation refers to the spinning of the object about an axis through the center of mass Ho, T.H. and Ahn, K.K., 2012. The vector of the angular velocity which points along the axis of rotation with some magnitude which is determined by the rate of change of the angle of rotation describes rotational motion. Every object exhibits not less than three mutually perpendicular directions that are mutually preferred and are known as the principal axes of rotation of the object. There is no change in the direction of rotation along a principal axis with time and should there be a change, then the motion will complicated Farimani, A.B., Wu, Y. and Aluru, N.R., 2013. The moment of inertia determines the properties of an object when rotating about a principal axis.
The kinetic energy of such a body that rotates around the principal axis is determined by the sum of the rotational energy and the translational energy of the body.
When the object is rolling, the speed of the center of mass, VCM, and the angular velocity have a relationship with the radius, R, of the object that is rolling using the rolling condition Farimani, A.B., Wu, Y. and Aluru, N.R., 2013
VCM=R
The amount and direction of rotational motion that can be contained within a rolling object with respect to the vector of the momentum is defined by the angular momentum vector L, which is determined by the equation L=I when the object is rotating about the principal axis having a moment of inertia I.
The angular momentum of the object can be changed through a force, F, acting on it which would have an effect and thus change the rate of rotation and the rotation axis. A torque, is generated when the force, F, is applied on a point that is displaced from the mass center by a vector, r Farimani, A.B., Wu, Y. and Aluru, N.R., 2013.
dL/dt=
it should be noted that is at right angles to both the arm of the lever, r and the force, F. for the case of isolated system of objects, the sum of the available torques on the object disappear. For such a case, the sum of the angular momentum Ltotal which is the sum over all the angle vectors Lk of each of the objects becomes a constant vector which does not change with respect to time. The level of constancy of the angular momentum, in addition to the conservation of energy and the momentum make up the three main conservation laws in mechanics Hadziioannou, C., et al 2012.
|
Task |
Hazards |
Associated Risks |
Existing risk controls |
Risk rating with existing controls |
||
|
Holding the equipment |
Dropping the equipment |
Injury to the foot due to the impact |
Securely holding the equipment using a secure grip or proper placement of the equipment to prevent it from falling |
C |
L |
R |
|
2 |
D |
M |
||||
|
Hanging the masses |
Dropping the mass |
Injury from the dropped mass |
Using a secure grip in holding the mass to prevent them from falling. |
3 |
D |
M |
|
Rotating the equipment |
Moving equipment knock objects and people |
Moving equipment causing injury due to knocking |
Keeping off the radius of the moving equipment |
2 |
D |
M |
Equipment used during the experiment
Procedure of the investigation
Note: the acceleration of the hanging mass in step 3 is from rest a height h that has an acceleration of a, striking the floor after time t
The results were as follows
Upon calculation, the absolute possible error in terms of the inertia of the hanging masses was 0.99%. This experiment however exceeded the theoretical values by a margin of 9.68% and owing to the fact that the percentage error falls off the bounds of error of the devices that were used; the big margin could be attributed to experimental errors Yurchenko, D., Naess, A. and Alevras, P., 2013. The error is expected to be even larger should the value of h be too small or the values of t, r or m are too large. Owing to the fact that the measurement of m and r were done on lee once and the values used throughout the experiment, it is vivid that they have no impact or contribution as a source of error in the experiment. On another hand, the measurement of h in as much as is sophisticated may not be a contributor to the error as well being that the method adopted remained unchanged throughout the experiment and the hanging masses provided accurate results Belfi, J. et al 2012. This leaves the most likely source of error in the experiment to be time. This could be as a result of a delay in the human reaction as well as owing to the fact that the results were obtained for the hanging masses Ho, T.H. and Ahn, K.K., 2012.
The accuracy of the experiment is determined by finding the average angular momentum of the three different masses that have been used as well as the sum average of their masses. The hanging mass whose angular momentum is close to the average angular momentum of the three hanging masses tends to be more accurate and the reverse is equally true.
As can be observed from the results of the experiment that has been performed above, a change in mass has an impact on the angular momentum of an object. Holding all the other factors constant, an increase in mass leads to a corresponding increase in the angular momentum. This means that angular momentum is directly proportional to the mass of an object Nagai, K. et al 2013.
The accuracy or high precision of the experiment would be achieved through various ways including improving on the human delay reaction to time which was the main source of error in the experiment. This is most achievable by performing the experiment in groups in which one does the setup of the experiment as another records the time Guan, M. and Liao, W.H., 2016.
Conclusion
The hanging mass experiment is a typical illustration of rotational motion in objects. An increase in the mass of an object increases the angular momentum while a decrease in the mass leads to a corresponding decrease in the angular momentum.
References
Belfi, J., Beverini, N., Bosi, F., Carelli, G., Di Virgilio, A., Maccioni, E., Ortolan, A. and Stefani, F., 2012. A 1.82 m 2 ring laser gyroscope for nano-rotational motion sensing. Applied Physics B, 106(2), pp.271-281
Berliner, L.J. and Reuben, J. eds., 2012. Spin labeling: theory and applications (Vol. 8). Springer Science & Business Media.
Farimani, A.B., Wu, Y. and Aluru, N.R., 2013. Rotational motion of a single water molecule in a buckyball. Physical Chemistry Chemical Physics, 15(41), pp.17993-18000.
Guan, M. and Liao, W.H., 2016. Design and analysis of a piezoelectric energy harvester for rotational motion system. Energy Conversion and Management, 111, pp.239-244
Hadziioannou, C., Gaebler, P., Schreiber, U., Wassermann, J. and Igel, H., 2012. Examining ambient noise using colocated measurements of rotational and translational motion. Journal of seismology, 16(4), pp.787-796
Ho, T.H. and Ahn, K.K., 2012. Design and control of a closed-loop hydraulic energy-regenerative system. Automation in Construction, 22, pp.444-458
Nagai, K.H., Takabatake, F., Sumino, Y., Kitahata, H., Ichikawa, M. and Yoshinaga, N., 2013. Rotational motion of a droplet induced by interfacial tension. Physical Review E, 87(1), p.013009.
Sun, W., Xu, A.G., Che, L.N. and Gao, Y., 2012. Accuracy improvement of SINS based on IMU rotational motion. IEEE Aerospace and Electronic Systems Magazine, 27(8), pp.4-10
Su, Y., Gömöry, P., Veronig, A., Temmer, M., Wang, T., Vanninathan, K., Gan, W. and Li, Y., 2014. Solar Magnetized Tornadoes: Rotational Motion in a Tornado-like Prominence. The Astrophysical Journal Letters, 785(1), p.L2.
Yurchenko, D., Naess, A. and Alevras, P., 2013. Pendulum’s rotational motion governed by a stochastic Mathieu equation. Probabilistic Engineering Mechanics, 31, pp.12-18
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