Laws of Motion ' Newton 's laws Momentum Conservation frame of Reference Free Body Pulley , Diagram Inclined Plane . Friction circular Motion 2- 2 Qts Newton 's First Law INERTIA • all bodies by of property virtue which cannot of they or motionchange rest their state Inherent : of : . 1st law : - . body continue to be in its state of rest OR motion along a straight line unless acted upon some external to the state A force change Newton 's Second rate The of change by . Law linear momentum of is directly proportional to external force applied this on body and change takes place always in direction of applied force . - - F dpdt x f - f- E = = ( kddtf DI = dt FORCE K . • Stops or changes ma = 2) d¥mJ • • - ) = m External Produces tries or to dat full or mat or push produce tries to stop tries to = motion moving body direction change . . IMPULSE F • = m = M a- ( Iz tz E Pz = ' tz - - Ft - - T ti f (ta p, t i - ti) = pz - Pg t =3 Impulse = linear in change momentum produced by forces . Newton 's 3rd Law • To every action opposite • - reaction There is always exert in different pairs on 3rd of Major Application Gun • • Recoiling of Jet aeroplanes an equal and . Action and reaction act Forces always movement . Law : bodies . of Momentum conservation 1-34 ' M, B M, Mz f, , ← Mz ↳ FT = 2 Mili , - µ, - it , ) = - Mz ( Tz Ta ) - t M = , VT Propulsion t MTV2 variable mass of Ejection of gas - = offs Cr) Thrust = a GUN Mz Mi FI , upward Recoil fz , uz , Rate → ↳ vz -t m UT + Maltz rocket = - - darfur offs Em - - = Vrcr) rime velocity of Fanfare firing ) vz → v ← Mz ' ph A Mi coifing of gun O = MIT II Mz t = - = Rafter firing? Tz mm÷T , Frame INERTIAL frame • of Reference FRAME Newton 's where Laws valid are . Any frame moving with constant velocity Earth 's frame is Inertial frame • • NON INERTIAL - Frame • Pseudo is force Accelerated • FRAME Newton's where laws not are valid . used frame • . A a. big B - l A Inertial : Tues O que g • B nos O - Tsin O tano mg = = = m Mg (o ) Fp ma : pseudoforce considered a- Tsin O p my - y yo Tsin O a Tues O Inertial non : g opposite to Tsin O NE ET 2019 Tues O tano = Eg Fp = - = mg motion ma I Free Body Diagram 1 Decide 2 Identify forces system 4 1- n n (by platform) 2 N Reaction bodies in ( by block) Nz Mp • not Sf platform ( by mg accelerating • Of system accelerates up Ca) • Of system accelerates II two Blocks Nz T ( by ( mzg • • T = Mg a = - Mpg Mg Mg - ( Mz X block MI M, t Mz = Nz Ma = N = Ma - Nz ( by each ground) string by string) by mi ) Acceleration of N Mg Mz Mi z - Nt down La) connected - ( by mpg earth) N . equations write I : normal Between Intact platform (Mp ) ground anis choose block M free body diagram Make 3 a string) Mz by m2 ) = Mzg FMas ( by t Mz ground ) f Tension III. en ' in block at from left → a → ← i → U → m → Tn n Tn f = MA = mcmass n - L for ) Mfl - n ) ( a 1¥ M2 M2 f a Mz F- = M, I a m a Tn =L a. f → m distance m = . 't M, + 72 Mz + = Mz M, t Mz tf 3 M38 fz=M3A =(m+M3m+m )f , :3 Mz f t Tz MZ " Mif = Mit Mz a →a " t m k (Mzt Mz) N3 Fz Mz Mz s F = t → Mz + Mz a T 73 Fz = (Mzt Mda =(mm.IT??mg)r- Pulley for my For Mz : . ou Mz T : a ne = @ i - - g - Mit Mz ) MIA = y Mza = Mzg ma (2mm;mmz)g T T g f - - maginn = Mzgsinp Mima t - Mzgsigg Mig Sina Mz ( Sina M , 1- M2 * Simp) La MI d . Mig may M, = p Migues Mig T mg 2 Maguey ^ ? , , d a. f N a N \ ma a 2T=4⇐ g Inclined Plane T - - n g Friction . opposing force Depends roughness Area The • on • Independent of • surface contact of . . Fk . . acts that of friction Static two bodies friction Kinetic kind between when a the N = coefficient of - body slides kinetic over friction a . friction kind of friction acting motion as N f= s . ↳ fsc tscmax, when Hs N f- s # - there fk no relative Reaction normal coefficient of Hs N is - static friction H kN y# - he • Friction • Lubrication is necessary evil Ball bearings reduce a , . friction . Angle of friction NI HSNNF tan f f a tan = x - - = as - a Angle of f- Mgmt a N f - tan ' ( Hs) repose Driving force mgsinx mgsina ' tana of . - Limiting friction HSN = uismgcosa = Hs = mg f- Sino f TO for movement f- Celso Fuego f 7 > HR 14mg case + Hsin O HN Fmin = Hmg I -1 O 142 - - tan ' (H) circular motion I Motion on Road Level N - mg N f £ = O mg = Hs N = MI R U2 HSRNV ! f M f Uman I Motion on Umin as = O Vmax ÷ Banked Road vmax if = =J¥ = = rgfys.t.tn:o) pig tan O I + - Ys Hs tan 0 Bending of Cyclist . tano - I Rg Impt . Previous Years