tag:blogger.com,1999:blog-556007631349067217.post7758030052433780737..comments2016-09-01T02:07:59.591-07:00Comments on VISUALIZING MATHS & PHYSICS : VECTORS: Significance &application of Cross product and dot product.BINNOYhttp://www.blogger.com/profile/16087091424947885602noreply@blogger.comBlogger8125tag:blogger.com,1999:blog-556007631349067217.post-90472624743450742402015-11-14T02:35:40.763-08:002015-11-14T02:35:40.763-08:00Hi,
Its a brilliant question that 'IN CASE OF ...Hi,<br />Its a brilliant question that 'IN CASE OF ELECTROMAGNETIC WAVE,...WHY ARE THEY CONSIDERING THE SIN(ANGLE)?<br /><br />To understand this.....just draw an electromagnetic wave on a paper.<br />Now after it is drawn....move a pencil along its borders.<br />What is noticed?<br /><br />1) The angle at which you have to move your hand changes as you move along varies( angle varies).<br />2) You find the angles or patterns repeating themselves after regular intervals (periodic motion).<br /><br />So lets say you are plotting this sin wave now on a graph.<br />You just have to do y = sin (x).<br />If you want some quantities instead of x and y.....just say time on x-axis and height of wave on y-axis....<br />then you can say that HEIGHT = sin (TIME)<br /><br />When time = 0 sec...height = sin(time) = sin(0) =0<br />When time = 90millisecons......height=sin(time) = sin(90) = 1.<br />When time = 180milliseconds...height = sin (time) = sin(180) =0<br />When time = 270milliseconds...height = sin(time) = sin(270) = 1.<br /><br />Now sin, i said is a measure of how much out of alignement one thing is with other. <br /><br />So just observe a sin wave....At 90 degrees...the wave is out of alignment w.r.t the y-axis and at 0 degrees...the wave is fully in alignment w.r.t the y-axis.<br /><br />Just draw a tangent to the wave when it is at 0 on the x-axis.....you will see the tangent is parallel to the y-axis....thus at x=0 the wave is 0% perpendicular to the y-axis ....hence sin(0) = 0.<br /><br />Just draw now a tangent to the wave when it is at 90 milliseconds....i.e at x = 90 milliseconds.<br />This tangent will be fully perpendicular ( fully out of alignment ) w.r.t the y-axis.<br /><br />And since sin( ) is a measure of how much perpendicular or out of alignment two forces are .......sin (90) = max = maximum height of the wave.<br /><br />Hope this helps <br />BinnoyBINNOYhttp://www.blogger.com/profile/16087091424947885602noreply@blogger.comtag:blogger.com,1999:blog-556007631349067217.post-88988395952901641162015-11-13T21:55:29.869-08:002015-11-13T21:55:29.869-08:00in case of electromagnetic wave ,why there conside...in case of electromagnetic wave ,why there considering the sin(angle)? Unknownhttp://www.blogger.com/profile/15670909594260020334noreply@blogger.comtag:blogger.com,1999:blog-556007631349067217.post-26767213595839592592015-07-21T09:52:41.126-07:002015-07-21T09:52:41.126-07:00Yeah......Good question.
Well Raghu......just ima...Yeah......Good question.<br /><br />Well Raghu......just imagine a boat which is square in size....yes square.<br />or cubical.<br /><br />Imagine such a cubical boat (from all sides cubical,...no curves nothing), such a boat moving through a river.<br /><br />The amount of friction will be more than a normally tapered boat right.<br /><br />Now just see where the friction will occuring....it will be occuring at that front end mainly of this cube which will be facing the water. <br /><br />This side of the cube where the water will be hitting is responsible for max friction. And this side is 90 degrees w.r.t to the direction at which water hits it.<br /><br />Now lets say you get frustuated with this huge friction and you decide to cut the front section of the boat such that it gets tapered at 60 degree w.r.t the direction at which water will hit it when the boat start moving.<br /><br />Because of the 60 degree tapering....the friction will reduce about sqrt(3)/2 times compared to that horribly designed cube of 90 deg at all sides.<br /><br />If you still want to make your boat more pointed....by cutting and tapering the front portion to say 30 deg....the friction will reduce further to half as compared to when your boat was a cube having 90 degree edges..<br /><br />But still why does this happen? Why doesnt the friction dissapear.<br /><br />It is because no matter how much steeply we curve the boat....there will be parts of it which will have to hit against the water.,,,,especially the front section of the boat.<br /><br />The more you make the front section perpendicular w.r.t the direction in which you are moving....more the friction.<br /><br />The more you make this front section tapering.....the lesser the friction.<br /><br />That is why they make jet planes and concorde and all having peak like front portions.<br /><br />If you make the front section of the boat infinitely thin....like a thin sheet...and then move it parallel to the flow of the river....its front portion is so thin....it will hardly hit water....<br /><br />So friction might be around nill....but not nill because this sheet still will have some thickness to it,<br /><br />So friction in case of a boat will come into play due to water hitting some section of your boat which lies somewhat perpendicular to the direction in which water will be hitting it .<br /><br />NOW WHY IS THAT AT IF YOU MOVE AT 180 DEGREES WITH RESPECT TO THE RIVER.....FRICTION WILL INCREASE..<br /><br />Well consider...two cases...<br /><br />case 1<br />You move in the same direction of the river....in this case....the water particles in the river and your boat , they are moving in the same direction....so the water particles will hit the front of your boat less vigirously. So you will feel the fury of these water particles less and so less friction.<br /><br /><br />Case 2<br />If you move in the opposite direction of the river.....the relative velocity between you and the water particles will be very high.<br />Now not only will the water particles hit you more vigirously<br />....but your boat also with its own velocity will hit the water in the river more vigirously..<br /><br />Its like if you collide into a person who was running in the opposite direction in which you were running....wont the impact be higher..<br /><br />On the other hand if you collide into a person who was running in the same direction in which you were running but somewhat slow....wont the impact be lower??<br /><br />So The fricition will be depending on two things..<br />1] How perpendicular the front section is w.r.t to the flow of water...(so a cross product here)<br /><br />2] How aligned you are with the flow of water...(so dot-product here).<br /><br />So the equation of friction will have i think cross-product and dot-product together.<br /><br />So it will have sin( ) and cos ( ) both in its equation.<br /><br /><br />A great question by the way!!!<br /><br /><br />Let me know if there are any further questions.<br /><br />Hope this helps<br />BinnoyBINNOYhttp://www.blogger.com/profile/16087091424947885602noreply@blogger.comtag:blogger.com,1999:blog-556007631349067217.post-68133638918425480472015-07-21T09:05:45.067-07:002015-07-21T09:05:45.067-07:00"Cross product comes into picture whenever tw..."Cross product comes into picture whenever two objects work against each other, completely out of line and produce maximum impact when perpendicular".<br /><br />I have some basic doubt...<br /><br /><br />|||| Now imagine the same boat and the same river, but this time instead of measuring the velocity of the river, you want to measure the friction between the boat and the river<br /><br />Friction will be maximum when boat goes in opposite to river flow... so it should be 180 degrees right... but how it produces maximum friction when 90 degrees.. <br />might be i misunderstood some simple concept... pls clear my doubt binnoy.. Thanks Raghuhttp://www.blogger.com/profile/08809712636517939891noreply@blogger.comtag:blogger.com,1999:blog-556007631349067217.post-83578890408102742502015-07-21T08:59:01.986-07:002015-07-21T08:59:01.986-07:00You are welcome Raghu
BinnoyYou are welcome Raghu<br />BinnoyBINNOYhttp://www.blogger.com/profile/16087091424947885602noreply@blogger.comtag:blogger.com,1999:blog-556007631349067217.post-9435293091521126022015-07-21T08:50:23.965-07:002015-07-21T08:50:23.965-07:00Thanks for the article... it is simple yet powerfu...Thanks for the article... it is simple yet powerful.... Its wonderful.... Hats off to you binnoyRaghuhttp://www.blogger.com/profile/08809712636517939891noreply@blogger.comtag:blogger.com,1999:blog-556007631349067217.post-67999108855038991002015-06-16T06:00:50.964-07:002015-06-16T06:00:50.964-07:00Thank you so much for your words.
BinnoyThank you so much for your words. <br />BinnoyBINNOYhttp://www.blogger.com/profile/16087091424947885602noreply@blogger.comtag:blogger.com,1999:blog-556007631349067217.post-90388344553035684842015-06-16T05:23:10.600-07:002015-06-16T05:23:10.600-07:00hello, thank you for embarking on this page. i was...hello, thank you for embarking on this page. i was beyond frustrated because i am an arts student and do not take physics. However, I have to take math and i could not see the LINK vectors had with anything but this helps! Or at least I see how vectors can be useful in real life. Your passion for the subject is commendable, keep it up! Anonymousnoreply@blogger.com