Formula sheet

Class 10–12 · Physics · Chemistry · Maths

1523/1523

Cl.SubjectNameFormula
11PhysicsAccelerationDer.a⃗=dv⃗dt=d2r⃗dt2\vec a=\dfrac{d\vec v}{dt}=\dfrac{d^2\vec r}{dt^2}
11PhysicsAcceleration of Centre of MassDer.a⃗CM=∑imia⃗iM=F⃗extM\vec a_{CM}=\dfrac{\sum_i m_i\vec a_i}{M}=\dfrac{\vec F_{ext}}{M}
12MathsAdjoint MatrixDer.Aadj⁡(A)=adj⁡(A)A=(det⁡A)IA\operatorname{adj}(A)=\operatorname{adj}(A)A=(\det A)I
12MathsAdjoint of MatrixDer.adj⁡(A)=[Cji]\operatorname{adj}(A)=[C_{ji}]
11MathsAlgebraic Operations of Complex NumbersDer.(a+ib)(c+id)=(ac−bd)+i(ad+bc)(a+ib)(c+id)=(ac-bd)+i(ad+bc)
11PhysicsAngle of ReposeDer.tan⁡θr=μs\tan\theta_r=\mu_s
11PhysicsAngular AccelerationDer.α=dωdt\alpha=\dfrac{d\omega}{dt}
11PhysicsAngular DisplacementDer.θ=sr\theta=\dfrac{s}{r}
12PhysicsAngular Frequency & Time PeriodDer.ω=2πf=2πT\omega=2\pi f=\dfrac{2\pi}{T}
11PhysicsAngular KinematicsDer.ω=ω0+αt,θ=ω0t+12αt2,ω2=ω02+2αθ\omega=\omega_0+\alpha t,\quad\theta=\omega_0t+\tfrac12\alpha t^2,\quad\omega^2=\omega_0^2+2\alpha\theta
11PhysicsAngular MomentumDer.L⃗=r⃗×p⃗,L=Iω (fixed principal axis)\vec L=\vec r\times\vec p,\quad L=I\omega\ \text{(fixed principal axis)}
11PhysicsAngular VelocityDer.ω=dθdt\omega=\dfrac{d\theta}{dt}
10MathsAP nth termDer.an=a+(n−1)da_n = a + (n-1)d
10MathsAP sum of n termsDer.Sn=n2[2a+(n−1)d]=n2(a+l)S_n = \dfrac{n}{2}\bigl[2a + (n-1)d\bigr] = \dfrac{n}{2}(a + l)
11PhysicsApparent Weight in a LiftDer.N=m(g±a)N=m(g\pm a)
12MathsArea of Triangle Using DeterminantsDer.Δ=12∣∣x1y11x2y21x3y31∣∣\Delta=\frac12\left|\begin{vmatrix}x_1&y_1&1\\x_2&y_2&1\\x_3&y_3&1\end{vmatrix}\right|
12ChemistryArrhenius equationDer.k=Ae−Ea/(RT)k = A e^{-E_a/(RT)}
11PhysicsAtwood MachineDer.a=(m2−m1)gm1+m2,T=2m1m2gm1+m2a=\dfrac{(m_2-m_1)g}{m_1+m_2},\quad T=\dfrac{2m_1m_2g}{m_1+m_2}
11PhysicsAverage PowerDer.Pavg=WΔtP_{avg}=\dfrac{W}{\Delta t}
12PhysicsAverage Power ConsumptionDer.Pavg=VrmsIrmscos⁡ϕP_{\rm avg}=V_{\rm rms}I_{\rm rms}\cos\phi
11PhysicsAverage SpeedDer.vavg,speed=total distancetotal timev_{avg,speed}=\dfrac{\text{total distance}}{\text{total time}}
11PhysicsAverage VelocityDer.v⃗avg=Δr⃗Δt\vec v_{avg}=\dfrac{\Delta\vec r}{\Delta t}
11PhysicsBallistic PendulumDer.u=M+mm2ghu=\dfrac{M+m}{m}\sqrt{2gh}
12PhysicsBandwidth & Half-Power FrequenciesDer.Δf=f2−f1=R2πL=f0Q\Delta f=f_2-f_1=\dfrac{R}{2\pi L}=\dfrac{f_0}{Q}
11PhysicsBanking of RoadsDer.tan⁡θ=v2rg\tan\theta=\dfrac{v^2}{rg}

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