Chpte. Review of Newton's Lws, Units nd Diensions, nd Bsic Physics You e ll fili with these ipotnt lws. But which e bsed on expeients nd which e ttes of definition? FIRST LAW n object oves unifoly (o eins t est) povided tht thee is no net foce cting on it. F = 0 no chnge in otion. One cn test this using expeient with n i hockey tble. When the tble is pefectly level, the puck will not ove! You hve to be vey ceful, howeve, bout the coodinte syste in which you obseve the object. If you e stnding on otting tble without being we of the ottion, you will see the object ove due to centifugl foce nd be puzzled! One is fee to choose ny coodinte syste he/she likes (fixed to tble, oving with the puck o stnding on the gound) but you hve to know wht it is. If coodinte syste is not cceleting, it is clled INERTIAL nd one lwys cn be found. This is the essence of FIRST LAW. This hs ipotnt iplictions in eteoology we study the wethe in efeence fe of the otting eth it is non-inetil efeence fe, nd thus Newton's lws (especilly the second) cn be pplied to the tosphee only if we tke into ccount the fct tht the coodinte syste (eth) is cceleting (due to constnt chnge of the diection of otion of objects on the eth sufce). This is whee Coiolis foce coes in, s we will see lte. Coiolis foce of one of the ost ipotnt foce fo lge scle tospheic flows! SECOND LAW Suppose we ttch ubbe bnd to ou i hockey puck. If we stetch it, the puck stts to ove, if we keep it stetched the se ount, wht is the esulting otion? The speed (elly the velocity) of the puck inceses unifoly with tie constnt cceletion. Now, eplce the light plstic puck with b of gold, now if we stetch the ubbe nd by the se ount, the cceletion will be uch diffeent f less in fct! So the cceletion depends upon fundentl popety of the object its ss. Let's define p = ss of the puck g = ss of the gold b
If we now esue (expeienttion is ipotnt!) the cceletion of the two sses long the line of cceletion, we will find tht p g g =, p We thus hve = p g p g which is ctully the definition of ss! Note tht it is lwys eltive gvity until we ssign vlue fo p. Tht is, if p 1 g, then we cn find g eltive to it. [The stndd of ss is etllic weight kept in Fnce.] To this point, we hve not elly defined how the puck o b is cceleted, but the stetching poduces n pplied foce. If we pply bnds on opposite sides of the puck, it doesn't ove! If we put two on the se side, it cceletes t twice the te. The foce How do we bing foce into the pictue? Let's sy tht 1 foce unit is wht is needed to poduce 1 unit of cceletion fo unit ss. Wht is 'unit ss'? It could be 1 kg o 1 g. Thus, F units of foce poduces F units (diffeent unit) of cceletion, i.e., F We lso know tht 1 if we define 1 F = then we hve units of cceletion F = o F = the fundentl eqution of NWP nd ll of eteoology! 4
This bove is the fili fo of Newton's Second Lw. Howeve, tht is not ll thee is to it. Point I: Pinciple of Supeposition Acceletion is Vecto (gnitude + diection), nd ss is Scl. So, foce hs to be vecto too F =. So, Newton's lw is elly -D! And, the cceletion is esult of the NET FORCE, i.e., the vecto su of ll foces. It's just like tug of w. n F = F = F + F + F +... + F = i= 1 i 1 n Point II: The nd lw is elly d Fnet = ( V) = (oentu)/ t dt whee V = velocity vecto. The foce intoduces chnge in oentu. F = ssues tht the ss of the object eins constnt, tht needn't to be the cse think of n i pcel tht is losing in wte content s it ises. We will study oentu lte. Point II: Foce is not tte of definition only. Foces lwys ise by vitue of intections ong systes of bodies, nd the intection is the significnt pt. All of ou discussion hs been fo isolted bodies, i.e., no noon, sts, etc. But, such intections e usully popotionl to 1/, so we cn educe the s uch s desied. Think of gvity, oe on this lte. THIRD LAW Foces lwys opete in pis so to evey ction thee is n equl nd opposite ection. Thee e no lone foces! If body exets F on body b, then body b exets F b on, nd F = - F b. Think of pushing ginst wll! Gvittion. Gvity is the ost fili of the fundentl foces (cope to e.g., electognetic foce). Newton ws esponsible fo showing how gvity woked, nd he did this in the context of plnety obits. He, t ge 6 (!), showed tht the ellipticl obits of plnets could be ccounted fo if evey pi of bodies hd ssocited with the foce of ttction popotionl to thei ss nd invesely popotionl to the Sque of the distnce between the. 5
b F b Fb F b By tking esueents, one cn deteine the constnt of popotionlity nd thus wite Gb F = Newton's Lw of Gvittion whee G = gvittionl constnt = 6.67 x 10-11 N kg -. The gvittionl foce F between pticles cts on line connection the centes of the pticles (o the cente of ss in cse of goup) nd is lwys ttctive. Gvity Conside now n object of ss t the sufce of the eth, whose ss is e. Then Ge F =, = dius of Eth. G Now, define e g F = g. Fo e = ss of eth nd its dius, g=9.80 s -. This bings out ysteious popety of the gvittionl foce the cceletion of pticle unde the influence of gvity is independent of its ss!! (not ieditely obvious does fethe flls to gound fste thn stone fo the se height?) g = cceletion due to gvity Befoe we get down to solving soe sple pobles, let's exine soe fundentl tools tht you will need. 6
Units nd Diensions The fundentl units e ss, length, nd tie (see hndout). The biggest hssle is oving fo one syste to nothe, though fotuntely, the wold in incesingly stnddizing on one syste.. CGS (centiete-g-second) used lot in ely dys of science nd engineeing b. MKS (ete-kilog-second) lso clled SI (Intentionl Syste of Units, Systèe Intentionl) the one of choice. Requied units of Aeicn Meteoologicl Society (AMS) Jounls! c. FPS (foot-pound-second) English units. Non-etic syste. Unfotuntely this county eins one of incesingly fewe counties who still sticks to it. Not even the English. See ticle on Ms Clite Obite it sys Units e vey ipotnt!! Mesueent nubes without unit e eningless nd cn led to disste! Consistency of Diensions The biggest point to be de hee is CONSISTENCY of diensions on both sides of n eqution. By checking fo this, you cn fequently uncove eos in you equtions nd/o solutions. Mke it hbit to check the diensions on both sides of equtions! Exple: Let's veify the gvittionl eqution Left hnd side: G F = 1 kg F ~ ~ s Right hnd side: G 1 = s kg = s kgkg kg consistent! In this clss, we will not use Newtons s the unit fo foce, but the kg /s. 7
kg Note tht = kg s -, eithe fo is oky, lthough the ltte is ecoended s fo of nottion of cetin Jounls, such those of AMS. Unit Convesions Exple: Convet ft ( lbs) hou to MKS. x ( ) ( ) 1 ft lbs ft lbs kg x hou = hou hou 1ft 1 lbs _ s All you hve to do is to fill the blnks fo the convesion fctos. Let's look t 1 ft ( lbs) hou : 1 ft ( lbs) hou =1 ( ) 1 0.45 1 ft lbs kg hou 1.04 10 hou.81ft = 1lbs 600s kg s 4 1 8