Physics Formulas for Class 11 and Class 12

1 |pg. 11 VectorsNotation:~a=ax +ay +az kMagnitude:a=|~a|= a2x+a2y+a2zDot product:~a ~b=axbx+ayby+azbz=abcos Cross product:~a~b~a ~b k~a ~b= (aybz azby) + (azbx axbz) + (axby aybx) k|~a ~b|=absin 2 KinematicsAverage and Instantaneous Vel. and Accel.:~vav= ~r/ t,~vinst=d~r/dt~aav= ~v/ t~ainst=d~v/dtMotion in a straight line with constanta:v=u+at, s=ut+12at2, v2 u2= 2asRelative Velocity:~vA/B=~vA ~vBProjectile Motion:xyOusin ucos u RHx=utcos , y=utsin 12gt2y=xtan g2u2cos2 x2T=2usin g, R=u2sin 2 g, H=u2sin2 2g3 Newton s Laws and FrictionLinear momentum:~p=m~vNewton s first law:inertial s second law:~F=d~pdt,~F=m~aNewton s third law:~FAB= ~FBAF rictional force:fstatic, max= sN, fkinetic= kNBanking angle:v2rg= tan ,v2rg= +tan 1 tan Centripetal force:Fc=mv2r, ac=v2rPseudo force.

2 ~Fpseudo= m~a0, Fcentrifugal= mv2rMinimum speed to complete vertical circle:vmin, bottom= 5gl, vmin, top= glConical pendulum:T= 2 lcos gmgTl 4 Work, Power and EnergyWork:W=~F ~S=FScos , W= ~F d~SKinetic energy:K=12mv2=p22mPotential energy:F= U/ xfor conservative , Uspring=12kx2 Work done by conservative forcesis path indepen-dent and depends only on initial and final points: ~Fconservative d~r= theorem:W= KMechanical energy:E=U+K. Conserved if forces areconservative in W t, Pinst=~F ~v5 Centre of Mass and CollisionCentre of mass:xcm= ximi mi, xcm= xdm dmCM of few useful ,m2separated byr:m1m2 Crm2rm1+m2m1rm1+m22.

3 Triangle (CM Centroid)yc=h3Ch3h3. Semicircular ring:yc=2r C2r r4. Semicircular disc:yc=4r3 C4r3 r5. Hemispherical shell:yc=r2 Crr26. Solid Hemisphere:yc=3r8Cr3r87. Cone: the height of CM from the base ish/4 forthe solid cone andh/3 for the hollow 2020 by Jitender Singh Ver. 2020 1 Get Our |pg. 2 Motion of the CM:M= mi~vcm= mi~viM, ~pcm=M~vcm, ~acm=~FextMImpulse:~J= ~Fdt= ~pCollision:m1m2v1v2 Before collisionAfter collisionm1m2v 1v 2 Momentum conservation:m1v1+m2v2=m1v 1+m2v 2 Elastic Collision:12m1v12+12m2v22=12m1v 12+12m2v 22 Coefficient of restitution:e= (v 1 v 2)v1 v2={1,completely elastic0,completely in-elasticIfv2= 0 andm1 m2thenv 1= 0 andm1 m2thenv 2= collision withm1=m2:v 1=v2andv 2= Rigid Body DynamicsAngular velocity: av= t, =d dt, ~v=~ ~rAngular Accel.}

4 : av= t, =d dt, ~a=~ ~rRotation about an axis with constant : = 0+ t, = t+12 t2, 2 02= 2 Moment of Inertia:I= imiri2, I= r2dmringmr2disk12mr2shell23mr2sphere25mr 2rod112ml2hollowmr2solid12mr2rectanglem( a2+b2)12abTheorem of Parallel Axes:I =Icm+md2cmI dIcTheorem of Perp. Axes:Iz=Ix+IyxyzRadius of Gyration:k= I/mAngular Momentum:~L=~r ~p,~L=I~ Torque:~ =~r ~F, ~ =d~Ldt, =I OxyP~r~F Conservation of~L:~ ext= 0 = ~L= condition: ~F=~0, ~ =~0 Kinetic Energy:Krot=12I 2 Dynamics:~ cm=Icm~ ,~Fext=m~acm, ~pcm=m~vcmK=12mvcm2+12 Icm 2,~L=Icm~ +~rcm m~vcm7 GravitationGravitational force:F=Gm1m2r2m1m2 FFrPotential energy:U= GMmrGravitational acceleration:g=GMR2 Variation of g with depth:ginside g(1 hR)Variation of g with height:goutside g(1 2hR)Effect of non-spherical earth shape ong:gat pole> gat equator( Re Rp 21 km)Effect of earth rotation on apparent weight.

5 Mg =mg m 2 Rcos2 Rm 2 Rcos mg~ Orbital velocity of satellite:vo= GMRE scape velocity:ve= 2 GMRK epler s laws:voaFirst:Elliptical orbit with sun at one of the :Areal velocity is constant. ( d~L/dt= 0).Third:T2 a3. In circular orbitT2=4 Simple Harmonic MotionHooke s law:F= kx(for small elongationx.)Acceleration:a=d2xdt2= kmx= 2xTime period:T=2 = 2 mkDisplacement:x=Asin( t+ )Velocity:v=A cos( t+ ) = A2 x2 Potential energy:U=12kx2 A0 AxUKinetic energyK=12mv2 A0 AxKTotal energy:E=U+K=12m 2A2 Get 2020 by Jitender Singh Ver. 2020 1 Get Our |pg. 3 Simple pendulum:T= 2 lglPhysical Pendulum:T= 2 ImglTorsional PendulumT= 2 IkSprings in series:1keq=1k1+1k2k1k2 Springs in parallel:keq=k1+k2k1k2 Superposition of two SHM s:~A1~A2~A x1=A1sin t, x2=A2sin( t+ )x=x1+x2=Asin( t+ )A= A12+A22+ 2A1A2cos tan =A2sin A1+A2cos 9 Properties of MatterModulus of rigidity:Y=F/A l/l, B= V P V, =FA Compressibility:K=1B= 1 VdVdPPoisson s ratio: =lateral strainlongitudinal strain= D/D l/lElastic energy:U=12stress strain volumeSurface tension:S=F/lSurface energy:U=SAExcess pressure in bubble: pair= 2S/R, psoap= 4S/RCapillary rise.

6 H=2 Scos r gHydrostatic pressure:p= ghBuoyant force:FB= V g= Weight of displaced liquidEquation of continuity:A1v1=A2v2v1v2 Bernoulli s equation:p+12 v2+ gh= constantTorricelli s theorem:vefflux= 2ghViscous force:F= AdvdxStoke s law:F= 6 rvFvPoiseuilli s equation:Volume flowtime= pr48 llrTerminal velocity:vt=2r2( )g9 Visit to buy IIT JEE Physics : Topic-wise Complete Solutions and our other books. Written by IITians, Forewordby Dr. HC Verma, Appreciated by 2020 by Jitender Singh Ver. 2020 1 Get Our Book