Category Archives: Youtube Car Reviews

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”

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”

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”

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”

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”

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”

The Valuation Game Read the valuation formula post for a more concise treatement using equations. But conceptually, the below should be the same. Without further ado, A company’s share price appreciation comes from three sources: (i) Lower expected rate of return for the same earnings. A 100$ recurring consistent quarterly earning is worth only $10,000Continue reading “The Valuation Game 101”

After the passing of Jack Bogle in 2019, the legendary founder of Vanguard index funds, it only seems fitting to address this topic here. The dual prongs of compounded costs in investing and the low chance of beating the market are the true merits of the index fund. An index fund does not seek toContinue reading “Rise of Index Funds & the Legend of Bogle”

The very initial phase I like to start a blog post with the very fundamentals because the simpler your ideas, the easier it is to get started. Feel free to skip down lower if this is too obvious. So what are shares and what do companies do? Companies make money by engaging in business activitiesContinue reading “What is the Stock Market 101”

Quaternions are generalized complex numbers that enable rotations in 3D rather than in just a complex plane. The complex number i is replaced by a general vector v which can be expressed in a 3D orthogonal basis i,j,k. The rules are defined as ijk=-1 and any basis squared is also minus one, like ordinary complexContinue reading “Hamilton’s Quaternions”