classical mechanics

Cross and Dot product of vectors.

Someone asked a very interesting question on the role of vectors in Physics. He was curious to know if dot product of vectors is natural but vector product is just syncretism, — that is make shift or unnatural manipulation.

Every vector can be resolved into two components. The cosine and sine components (any two vectors would constitute a plane) while cos part can represent the projection defined through dot PDT we can’t leave out the sine part. It plays its role through the vector or cross PDT.

The vector direction is no more along same direction as original vectors because of orthogonality. To preserve symmetry of both orthogonal components (or equal footing of both vectors, vector a and b eg) we need the 3rd dimension. Hence such a definition of cross PDT.

Eg the emf generated in a changing “mag field” (Faraday’s law) depends on change in mag field if area is held const. It also depends on change in “area vector” if mag field is held const. So there are two vectors involved and their transverse values matter (and not their longitudinal values). To preserve equivalent role of both area and mag field vectors the resultant vector must be in a 3rd orthogonal direction …

Also think of this; a scalar is not necessarily directionless. (think electric current or even temperature or heat gradient etc) They just do not have the full fledged capacity of vectors. Its like flower bud vs fully blossomed flower.

So scalars can’t be added like vectors. We tend to make a mistake here. We say scalars don’t have a direction. That’s totally erroneous. They do have direction and it matters. Which direction you want to stick to if the current flows along certain direction only?

Lets make it still more clear.

If there are two directions in which there are electric currents, we say they are both equal, the direction won’t matter. That’s where we make the mistake. We should say they are equivalent and not equal. Equality is ideal, its mathematical. But equivalence is physical. Its the effects of both currents in a certain sense that make them equivalent, but their strict equality does not follow.

Coriolis Force; an interesting idea

Coriolis Force
The article is 5.34 K worded. 

I have been thinking of writing a basic introduction, on this important physical concept — of, what’s known as a Coriolis force.

It is one of the interesting ideas of physics, which does not get as much of a mention perhaps, unless you just happen to know this, because of your advance footing, in the discourses of physics.

This is perhaps so because its two orders of magnitude smaller, in its strength, compared to relevant forces, in a situation, that involves this small — but its a significantly measurable force.

So, what’s a Coriolis Force?

I presume that most of us would be aware of, what’s a centrifugal force. Its in this context, that, a Coriolis force is most understandable.

So, what’s a centrifugal force?

A Centrifugal force, comes into picture, every time a centripetal force comes into consideration. A centrifugal force is the corresponding pseudo-force, of a centripetal force. So, for every centripetal force there would be a corresponding centrifugal force.

So, we need to shed light on a few things, before we understand, what is a Coriolis force. We need to, therefore, discuss; what are pseudo forces and what’s a centripetal or a centrifugal force, then a Coriolis force would be clearer, to the root.

So lets begin with force. 

Force has a basic standing in physics, in connection to, in what frames of reference we need to measure such a physical quantity, as are all other physical quantities to be measured, have a significance, as to in what frames of reference we are measuring those quantities in.

Solutions to Irodov problems

Problems In General Physics, 
I.E. Irodov
Part-I Physical Fundamentals in Mechanics.

Chapter 1.1 Kinematics.  

10 interesting problems in elementary mechanics

This post intends to provide 40 interesting problems in elementary mechanics from IE Irodov, Problems in general physics that I solved in last couple weeks. Note that another 30 problems (additional 12 at hand) which has been solved will be uploaded after they are scanned, shortly.

Basic Concepts.
In this class today we will discuss the subject of “kinematics” briefly and solve some problems, based on the same. 

The motion of objects are studied under the heading “mechanics”.

♣ Mechanics is called “kinematics” if we study about the “nature of motion” without regard to what factors are causing such motion. 

♣ In addition to kinematics, when we focus our attention to study the factors that cause motion, such is named as dynamics. 

In kinematics today we will discuss a few problems that will cover the topics of …