Re: Question
Naaw, he's not late, he just needs to up the voltage a bit.....<br /><br />Here's the real answer:<br /><br />--------------------------------<br />Newton's 2nd Law & Coriolis force <br />Newton's 2nd Law of Mechanics <br />F = M * A <br />M = mass of an object , kg <br />A = absolute acceleration<br />F = total actual force acting on the object;<br />unit : kg * m / (s**2)<br />F and A are both vectors <br /><br />reference frame , <br />* Absolute acceleration of an object is measured <br />in a reference frame at rest :<br />Such coordinate is called ( Inertial Coordinate) <br />* Such V is absolute velocity & A is absolute acceleration. <br />* wind is NOT absolute velocity <br />It is not measured in an inertial coordinate <br />* wind is a measure of the velocity of air parcels relative to a weather station ;<br />i.e. relative to a location on a rotating earth ,<br />Hence wind is a velocity in a Rotating Coordinate <br />It is a relative velocity . <br />* A change of wind is a relative acceleration <br />* if A refers to the relative (instead of absolute) acceleration in the formula above,<br />F would refer to more than just the actual force <br />We need to consider the effects associated with the rotation of the earth.<br />Those effects are called "forces" & <br />we include them in "F"<br /><br />Forces that affect wind : <br />(1) Coriolis force <br />(2) Centrifugal force <br />(3) Pressure gradient force <br />(4) Gravitational force <br />(5) Frictional force <br /><br />How to analyse/understand the nature of wind measured on earth? <br />To begin with, we need to introduce a force called <br />Coriolis Force <br /><br />F(Coriolis)<br />= 2 * V * W * sin f <br /><br />where V = wind speed <br />W = rotation rate of the earth,<br />one revolution per day <br />f = latitude <br />The dependence of latitude appears because only the local vertical component of the earth's rotation affects the horizontal wind. <br /><br />Direction of F(Coriolis) is 90 degree to the right of the wind vector in Northern Hemisphere. <br />e.g. F(Coriolis) is southward if the wind is westerly ; <br />Opposite in southern hemisphere .<br />F(Coriolis) only tends to change the direction of the wind & does not change the wind speed. <br /><br />What is the physical nature of F(Coriolis) ? <br />We can get a deeper understanding of F(Coriolis) by <br />relating it to the basic notion of "conservation of angular momentum" . <br /><br />Illustrated with a simple example : <br />Coriolis demo<br />* two players, A and B, standing at opposite sides of a merry-go-round that rotates in counterclockwise direction, <br />* A throws a ball straight towards B <br />* B cannot catch the ball since it goes to the right of B . <br />* B would conclude that the ball has been deflected <br />to the right presumably by a certain force. <br /><br />* Note : A & B are on a rotating coordinate <br />The rotational movement of an object with respect to an axis has a property called "Angular Momentum" <br /><br />absolute angular momentum<br />= (absolute tangential velocity) <br />* (distance from the axis of rotation) <br /><br />"tangential velocity" is the component of the velocity<br />in the direction of the curve of rotation. <br /><br />absolute tangential velocity of the ball<br />= relative tangential velocity of ball <br />+ tangential velocity due to merry-go-round <br /><br />Newton's law of motion implies that,<br />if there is no force acting on the ball,<br />its absolute angular momentum would not change. <br /><br />* Recall, A throws a ball radially towards B <br />* When the ball leaves A's hand,<br />the ball has zero relative tangential velocity; <br />it only has the velocity of the merry-go-round <br />* initial absolute tangential velocity<br />= the velocity of merry-go-round at A's position<br /><br />* The original amount of absolute angular momentum in the ball does not change <br />after it leaves A's hand because no real force acts on it thereafter. <br />i.e. Conservation of absolute angular momentum <br />* As soon as the ball leaves A's hand,<br />its distance to the axis of the merry-go-round decreases.<br />* This means that its new angular momentum associated with <br />the rotation of the coordinate becomes smaller. <br />* For the absolute angular momentum to remain the same,<br />the ball's relative angular momentum must increase <br />to make up for the difference <br />* Consequentially, a nonzero relative tangential velocity of the ball would appear; <br />i.e. The ball begins to move tangentially from its initial radial path ; <br />hence deflecting to the right . <br />* To A & B there appears to be a force <br />(first recognised by a French engineer, Coriolis)<br />causing the deflection.<br /><br />* a person standing on the ground is not on such a rotating coordinate; <br />he sees a ball going straight. <br />To him, there is no Coriolis force acting on the ball. <br />* Coriolis force also referred to as an apparent force; <br />Only apparent to observers on a rotating coordinate . <br /><br />* rotation of the earth is very slow compared with that of the merry-go-round <br />Hence its effect on the ball is negligibly small,<br />compared to the effect of the rapidly rotating merry-go-round <br />as far as A & B are concerned<br /><br />How might one describe what happens<br />to an air parcel moving in a curved trajectory ? <br />e.g. wind near a trough <br />Two equivalent points of view : <br /><br />(1) One could say that<br />the parcel has a centripetal acceleration. <br />A(centripetal) = V**2 / R <br />where V= speed of parcel <br />Its direction is 90 degrees to the "inside of the trajectory", called inward normal <br />R = radius of curvature <br /><br />(2) Alternatively, one could say that <br />there is a centrifugal force acting on the parcel. <br />The direction of this force is outward normal to the trajectory. <br />with a magnitude <br />F(centrifugal) = V **2 / R <br />Interpretation (2) is often used ,for convenience, e.g. when we discuss the balance of forces acting on air parcels later on. <br /><br />question for thought : <br />Why doesn't the moon crash down on earth under the influence of the gravitational force of the earth ?
