When a child swings on a swing, have you ever thought how it is possible without touching the ground. There is nothing to push off against.. a naive application of conservation of momentum might indicate that it is not even possible to start swinging! So how does it work? The catch is twofold. The firstContinue reading “How does a Swing work”
Author Archives: jjk7
Godel’s (first) incompleteness theorem
I would like to describe a most amazing result in math, computer science, logic and even philosophy (kind of a stretch there but..). Godel’s incompleteness theorem addresses the theory of natural numbers constructed from axioms. The results also apply to any equivalent theory and state that if, The axioms of the theory are consistent TheContinue reading “Godel’s (first) incompleteness theorem”
Noether’s theorem and Hamiltonian Formulation
This is a continuation to the previous post on Lagrange Formulation. If the Lagrangian does not depend explicitly on time, then becuase the partial time derivative is zero, the change or total time derivative of the Lagrangian can be non-zero only because of motion (change in coordinate values; not to be confused with a coordinateContinue reading “Noether’s theorem and Hamiltonian Formulation”
Musings on Phase and Configuration Space
Phase space communicates both the motion and configuration (location with shape) of a system (x1,x2, x1‘,x2‘), wheras configuration space only mentions the values of the degrees of freedom of the system, therby decribing its location and configuration (x1,x2). Clearly the number of entries in the configuration space will be equal to the number of degreesContinue reading “Musings on Phase and Configuration Space”
Fermat’s principle – Least Action for Light
The principle of stationary action from the previous post on Lagrangian mechanics can also be used outside pure mechanics. For example, for traveling light, including when it undergoes reflection or refraction. In this case, the action is not an energy but rather the time taken to traverse the distance under consideration. The principle states thatContinue reading “Fermat’s principle – Least Action for Light”
The Lagrange Formulation
I would like to describe the powerful method of Langrange-Euler equation in classical physics as opposed to directly applying Newtons laws. It is inherently an energy formulation but the results contain a few nuances. In the Lagrange formulation, the energy used is not the total energy, rather the delta of forms of energy. Let TContinue reading “The Lagrange Formulation”
The power of the inverse square law
Pursuant to the preivous post on the pythagoras theorem, we continue asking ‘why’, in this series of posts. I attempt to share my feeble understanding of why electric forces and gravitational forces closely obey the inverse square law in classical physics. I like the graivational wave interpretation. Simply put, this pins the cause on theContinue reading “The power of the inverse square law”
An intuitive proof of the Pythagoras theorem
There is a theorem so powerful in geometry, that it lies at the heart of not only geometry, but also coordinate geometry, trigonometry, algebra, vector physics and more! I am talking about an ancient theorem known ages ago, called in modern day by a name none other than the Pythagorean theorem. I am going toContinue reading “An intuitive proof of the Pythagoras theorem”
Home Value
Debate: A personal home is an investment My take : I agree it is an investment, but not a good investment always. Let me explain. If you are personally living in the home, you are consuming all your potential rental income. Consumption does not equal investment. If you save money on rent that you wouldContinue reading “Home Value”
The Growth Valuation Formula
What is the value of a stock (price)? It comes from the earnings it generates! Let us first consider constant earnings and then growing earnings. Constant Earnings P = E/r , where P is the price of the stock determined by the earnings potential E. This formula follows from the definition of the expected rateContinue reading “The Growth Valuation Formula”
Cars and Physics 