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MECHANICS UNIT 6
Motion of a particle under a central force field
Author of this note Mr. K. Prasad BSc from University of Calicut, MSc from university of Delhi, and M.B.A from IGNOU Delhi, These notes were prepared during my teaching session for under graduate students (11 Th and 12 Th class) of my school physics department. This note is helpful for under graduate students and junior level graduates. I declare that these notes are my original works based on my knowledge in physics and the books mentioned below are the reference books I used for preparing these notes
Table of contents (1) Motion of a particle under a central force (2) Angular momentum of a particle (3) Angular momentum formula (4) Kinetic energy and total energy (5) Kinetic energy definition (6) Energy definition (7) Energy equation and energy diagram (8) Kepler's laws (9) Kepler's first law (10)Kepler's second law (11) Kepler's third law (12)Satellite in circular orbit (13)Geosynchronous orbits. Reference Books: An Introduction to Mechanics, Daniel Kleppner& Robert Kolenkow, 2007, TataMcGrawHill Mechanics, DS Mathur, PS Hemne, 2012, S. Chand University Physics, FW Sears, MW Zemansky& HD Young 13/e, 1986, AddisonWesley Mechanics Berkeley Physicscourse,v.1: Charles Kittel,et.al.2007, TataMcGrawHill Physics – Resnick, Halliday & Walker 9/e, 2010, Wiley Engineering Mechanics, Basudeb Bhattacharya, 2nd edn., 2015, Oxford UniversityPress University Physics, Ronald Lane Reese, 2003, Thomson Brooks/Cole
Kinetic energy definition The kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains its kinetic energy unless its speed changes. The same amount of work is done by the body in decelerating from its current speed to a state of rest. Kinetic energy can be calculated as mentioned below
KE = 0.5 x m x v
2 KE is the kinetic energy m is the mass and v is the velocity Energy definition Energy is the capacity to perform work. Energy can neither made nor destroyed, and it must be changed starting with one structure then onto the next. The unit of Energy is equivalent as of Work, for example Joules. Energy is tracked down in numerous things, and along these lines there are various sorts of energy. All types of energy are either kinetic or potential. The energy moving is known as Kinetic Energy, while Potential Energy is the energy stored in an object and is estimated by how much work done. Energy equation and energy diagram The equation developed by Albert Einstein, which is usually given as E = mc2, showing that, when the energy of a body changes by an amount E (no matter what form the energy takes), the mass (m) of the body will change by an amount equal to E/c2. Energy diagram
Kepler's laws There are three laws by Kepler as mentioned below Kepler's laws First Law : Planetary orbits are elliptical with the sun at a focus. Second Law : The radius vector from the sun to a planet sweeps equal areas in equal times. Third Law: The ratio of the square of the period of revolution and the cube of the ellipse semi major axis is the same for all planets. Kepler's first law Kepler's first law - sometimes referred to as the law of ellipses - explains that planets are orbiting the sun in a path described as an ellipse. An ellipse can easily be constructed using a pencil, two tacks, a string, a sheet of paper and a piece of cardboard. Kepler's second law Kepler's second law states that a planet moves in its ellipse so that the line between it and the Sun placed at a focus sweeps out equal areas in equal times. Kepler's third law This law is known as the law of Periods. The square of the time period of the planet is directly proportional to the cube of the semi major axis of its orbit. Satellite in circular orbit
