Exhaustive Physics Formula Sheet for Class 11 & 12 (CBSE)

Saral Physics Formula Sheet

This comprehensive Physics Formula Sheet contains important Class 11 and Class 12 Physics formulas for CBSE examinations, competitive examinations and quick revision.

Class 11 Physics

1. Units and Measurements

Absolute Error: \( |\Delta a| = |a_{\text{measured}} - a_{\text{true}}| \)
Mean Absolute Error: \( \overline{\Delta a} = \frac{\sum |\Delta a_i|}{n} \)
Relative Error: \( \frac{\overline{\Delta a}}{a_{\text{true}}} \)
Percentage Error: \( \left( \frac{\overline{\Delta a}}{a_{\text{true}}} \right) \times 100\% \)
Error in Combination:
- Sum/Difference: \( \Delta z = \Delta x + \Delta y \)
- Product/Quotient: \( \frac{\Delta z}{|z|} = \frac{\Delta x}{|x|} + \frac{\Delta y}{|y|} \)
- Power: \( \frac{\Delta z}{|z|} = n\frac{\Delta x}{|x|} \)
Dimensional Formula: Velocity = \( [M^0L^1T^{-1}] \), Force = \( [M^1L^1T^{-2}] \), Energy = \( [M^1L^2T^{-2}] \)
Conversion: \( n_1u_1 = n_2u_2 \)

2. Motion in a Straight Line

Displacement: \( \Delta x = x_2 - x_1 \)
Average Speed: \( v_{\text{avg}} = \frac{\text{Total Distance}}{\text{Total Time}} \)
Average Velocity: \( \vec{v}_{\text{avg}} = \frac{\Delta\vec{x}}{\Delta t} \)
Instantaneous Velocity: \( v = \frac{dx}{dt} \)
Instantaneous Acceleration: \( a = \frac{dv}{dt} = \frac{d^2x}{dt^2} \)
Equations of Motion:
- \( v = u + at \)
- \( x = ut + \frac{1}{2}at^2 \)
- \( v^2 = u^2 + 2ax \)
- \( x_n = u + \frac{a}{2}(2n-1) \)
Free Fall: \( g = 9.8\,\text{m/s}^2 \)
Relative Velocity: \( v_{AB} = v_A - v_B \)

3. Motion in a Plane

Vector Resolution: \( A_x = A\cos\theta \), \( A_y = A\sin\theta \)
Magnitude: \( A = \sqrt{A_x^2 + A_y^2} \)
Direction: \( \tan\theta = \frac{A_y}{A_x} \)
Unit Vector: \( \hat{A} = \frac{\vec{A}}{A} \)
Vector Addition: \( \vec{R} = \vec{A} + \vec{B} \)
Resultant Magnitude: \( R = \sqrt{A^2+B^2+2AB\cos\theta} \)
Dot Product: \( \vec{A}\cdot\vec{B} = AB\cos\theta \)
Cross Product: \( \vec{A}\times\vec{B} = AB\sin\theta\,\hat{n} \)
Horizontal Projectile:
- Time of Flight: \( t = \sqrt{\frac{2h}{g}} \)
- Range: \( R = u\sqrt{\frac{2h}{g}} \)
- Velocity at Ground: \( v = \sqrt{u^2+2gh} \)
Oblique Projectile:
- Time of Flight: \( T = \frac{2u\sin\theta}{g} \)
- Maximum Height: \( H = \frac{u^2\sin^2\theta}{2g} \)
- Horizontal Range: \( R = \frac{u^2\sin2\theta}{g} \)
- Maximum Range: \( R_{\max} = \frac{u^2}{g} \)
Uniform Circular Motion: \( a_c = \frac{v^2}{r} = \omega^2r \)

4. Laws of Motion

Newton's First Law: \( \vec{F}_{net}=0 \Rightarrow \vec{v}=\text{constant} \)
Newton's Second Law: \( \vec{F} = \frac{d\vec{p}}{dt} = m\vec{a} \)
Momentum: \( \vec{p}=m\vec{v} \)
Impulse: \( \vec{J} = \int\vec{F}\,dt = \Delta\vec{p} \)
Newton's Third Law: \( \vec{F}_{AB} = -\vec{F}_{BA} \)
Conservation of Momentum: \( \vec{p}_{initial} = \vec{p}_{final} \)
Friction:
- Static Friction: \( f_s\leq\mu_sN \)
- Kinetic Friction: \( f_k=\mu_kN \)
- Rolling Friction: \( f_r=\mu_rN \)
- Angle of Friction: \( \tan\theta=\mu \)
Normal Force on Inclined Plane: \( N=mg\cos\theta \)
Apparent Weight in Lift: \( R=m(g\pm a) \)

5. Work, Energy and Power

Work: \( W = Fd\cos\theta \)
Variable Force: \( W = \int_{x_i}^{x_f}F(x)\,dx \)
Kinetic Energy: \( KE = \frac{1}{2}mv^2 \)
Work-Energy Theorem: \( W_{net} = \Delta KE \)
Gravitational Potential Energy: \( PE=mgh \)
Elastic Potential Energy: \( PE=\frac{1}{2}kx^2 \)
Mechanical Energy Conservation: \( \Delta KE+\Delta PE=0 \)
Power: \( P= \frac{dW}{dt} = \vec{F}\cdot\vec{v} \)
Average Power: \( P_{avg}=\frac{W}{\Delta t} \)
Coefficient of Restitution: \( e = \frac{v_2'-v_1'}{u_1-u_2} \)

6. System of Particles and Rotational Motion

Center of Mass: \( \vec{r}_{cm} = \frac{\sum m_i\vec{r_i}}{\sum m_i} \)
Velocity of Center of Mass: \( \vec{v}_{cm} = \frac{\sum m_i\vec{v_i}}{\sum m_i} \)
Moment of Inertia of Point Mass: \( I=mr^2 \)
Rod About Center: \( I=\frac{1}{12}ML^2 \)
Rod About End: \( I=\frac{1}{3}ML^2 \)
Disc About Center: \( I=\frac{1}{2}MR^2 \)
Ring About Center: \( I=MR^2 \)
Solid Sphere: \( I=\frac{2}{5}MR^2 \)
Parallel Axis Theorem: \( I=I_{cm}+Md^2 \)
Torque: \( \vec{\tau} = \vec{r}\times\vec{F} = I\vec{\alpha} \)
Angular Momentum: \( \vec{L}=I\vec{\omega} \)
Rotational Kinetic Energy: \( KE=\frac{1}{2}I\omega^2 \)
Rolling Motion: \( v=r\omega \)

7. Gravitation

Universal Law of Gravitation: \( F=G\frac{m_1m_2}{r^2} \)
Gravitational Field: \( \vec{g} = -\frac{GM}{r^2}\hat{r} \)
Gravitational Potential: \( V=-\frac{GM}{r} \)
Potential Energy: \( U=-\frac{Gm_1m_2}{r} \)
Orbital Velocity: \( v_o=\sqrt{\frac{GM}{r}} \)
Satellite Time Period: \( T= 2\pi\sqrt{\frac{r^3}{GM}} \)
Escape Velocity: \( v_e=\sqrt{2gR} \)
Kepler's Third Law: \( T^2\propto a^3 \)

8. Mechanical Properties of Solids

Stress: \( \sigma=\frac{F}{A} \)
Longitudinal Strain: \( \epsilon=\frac{\Delta L}{L} \)
Young's Modulus: \( Y=\frac{FL}{A\Delta L} \)
Bulk Modulus: \( B=-\frac{\Delta P}{\Delta V/V} \)
Shear Modulus: \( G=\frac{\tau}{\phi} \)
Hooke's Law: \( F=-kx \)

9. Mechanical Properties of Fluids

Pressure: \( P=\frac{F}{A} \)
Hydrostatic Pressure: \( P=P_0+\rho gh \)
Buoyant Force: \( F_b=V\rho_lg \)
Continuity Equation: \( A_1v_1=A_2v_2 \)
Bernoulli Equation: \( P+ \frac{1}{2}\rho v^2+ \rho gh = \text{constant} \)
Torricelli Theorem: \( v=\sqrt{2gh} \)
Stokes Law: \( F_d=6\pi\eta rv \)
Terminal Velocity: \( v_t= \frac{2r^2(\rho-\sigma)g}{9\eta} \)
Capillary Rise: \( h= \frac{2T\cos\theta}{\rho gr} \)

10. Thermal Properties of Matter

Heat Capacity: \( C=\frac{Q}{\Delta T} \)
Specific Heat: \( c=\frac{C}{m} \)
Heat Transfer: \( Q=mc\Delta T \)
Latent Heat: \( Q=mL \)
Linear Expansion: \( \Delta L=L\alpha\Delta T \)
Area Expansion: \( \Delta A=2\alpha A\Delta T \)
Volume Expansion: \( \Delta V=3\alpha V\Delta T \)
Thermal Resistance: \( R=\frac{l}{kA} \)
Stefan-Boltzmann Law: \( P=\sigma AeT^4 \)
Wien's Displacement Law: \( \lambda_mT=b \)

11. Thermodynamics

First Law: \( \Delta Q=\Delta U+\Delta W \)
Work Done: \( W=\int P\,dV \)
Isobaric Work: \( W=P\Delta V \)
Isothermal Work: \( W=nRT\ln\frac{V_2}{V_1} \)
Internal Energy: \( \Delta U=nC_v\Delta T \)
Mayer's Relation: \( C_p=C_v+R \)
Specific Heat Ratio: \( \gamma=\frac{C_p}{C_v} \)
Adiabatic Relation: \( PV^\gamma=\text{constant} \)
Carnot Efficiency: \( \eta=1-\frac{T_2}{T_1} \)

12. Kinetic Theory of Gases

Ideal Gas Equation: \( PV=nRT=NkT \)
Pressure: \( P=\frac{1}{3}\rho v_{rms}^2 \)
RMS Speed: \( v_{rms}=\sqrt{\frac{3RT}{M}} \)
Average Speed: \( v_{avg}=\sqrt{\frac{8RT}{\pi M}} \)
Most Probable Speed: \( v_{mp}=\sqrt{\frac{2RT}{M}} \)
Average Kinetic Energy: \( KE=\frac{3}{2}kT \)

13. Oscillations

SHM Equation: \( \frac{d^2x}{dt^2}+\omega^2x=0 \)
Displacement: \( x=A\sin(\omega t+\phi) \)
Velocity: \( v=\omega\sqrt{A^2-x^2} \)
Acceleration: \( a=-\omega^2x \)
Angular Frequency: \( \omega=2\pi f=\frac{2\pi}{T} \)
Spring Time Period: \( T=2\pi\sqrt{\frac{m}{k}} \)
Simple Pendulum: \( T=2\pi\sqrt{\frac{l}{g}} \)
Energy in SHM: \( E=\frac{1}{2}kA^2 \)

14. Waves

Wave Equation: \( y=A\sin(kx-\omega t+\phi) \)
Wave Number: \( k=\frac{2\pi}{\lambda} \)
Frequency: \( f=\frac{1}{T} \)
Wave Speed: \( v=f\lambda \)
String Wave Speed: \( v=\sqrt{\frac{T}{\mu}} \)
Sound Intensity Level: \( \beta=10\log\frac{I}{I_0} \)
Beat Frequency: \( f_b=|f_1-f_2| \)
Doppler Effect: \( f'=f\frac{v\pm v_o}{v\mp v_s} \)

Class 12 Physics

1. Electric Charges and Fields

Quantisation of Charge: \( q = ne \)
Coulomb's Law: \( F = \frac{1}{4\pi\varepsilon_0} \frac{q_1q_2}{r^2} \)
Vector Form of Coulomb's Law: \( \vec{F}_{12} = \frac{1}{4\pi\varepsilon_0} \frac{q_1q_2}{r^2}\hat{r}_{12} \)
Electric Field: \( \vec{E} = \frac{\vec{F}}{q_0} \)
Electric Field Due to Point Charge: \( E = \frac{1}{4\pi\varepsilon_0} \frac{q}{r^2} \)
Electric Dipole Moment: \( \vec{p} = q(2\vec{a}) \)
Electric Field on Axial Position of Dipole: \( E = \frac{1}{4\pi\varepsilon_0} \frac{2p}{r^3} \)
Electric Field on Equatorial Position of Dipole: \( E = \frac{1}{4\pi\varepsilon_0} \frac{p}{r^3} \)
Torque on Electric Dipole: \( \vec{\tau} = \vec{p}\times\vec{E} \)
Electric Flux: \( \Phi_E = \vec{E}\cdot\vec{A} = EA\cos\theta \)
Gauss's Law: \( \Phi_E = \frac{q_{\text{enclosed}}}{\varepsilon_0} \)
Electric Field Due to Infinite Line Charge: \( E = \frac{\lambda}{2\pi\varepsilon_0r} \)
Electric Field Due to Infinite Plane Sheet: \( E = \frac{\sigma}{2\varepsilon_0} \)
Electric Field Outside Charged Spherical Shell: \( E = \frac{1}{4\pi\varepsilon_0} \frac{Q}{r^2} \)
Electric Field Inside Charged Spherical Shell: \( E = 0 \)

2. Electrostatic Potential and Capacitance

Electric Potential: \( V = \frac{W}{q} \)
Potential Due to Point Charge: \( V = \frac{1}{4\pi\varepsilon_0} \frac{q}{r} \)
Potential Due to System of Charges: \( V = \frac{1}{4\pi\varepsilon_0} \sum\frac{q_i}{r_i} \)
Potential Due to Electric Dipole: \( V = \frac{1}{4\pi\varepsilon_0} \frac{p\cos\theta}{r^2} \)
Potential Difference: \( V_B-V_A = -\int_A^B\vec{E}\cdot d\vec{l} \)
Potential Energy of Two Charges: \( U = \frac{1}{4\pi\varepsilon_0} \frac{q_1q_2}{r} \)
Potential Energy of Electric Dipole: \( U = -\vec{p}\cdot\vec{E} \)
Capacitance: \( C = \frac{Q}{V} \)
Parallel Plate Capacitor: \( C = \frac{\varepsilon_0A}{d} \)
Capacitor with Dielectric: \( C = \frac{K\varepsilon_0A}{d} \)
Capacitors in Series: \( \frac{1}{C_{\text{eq}}} = \frac{1}{C_1} + \frac{1}{C_2} + \cdots \)
Capacitors in Parallel: \( C_{\text{eq}} = C_1+C_2+\cdots \)
Energy Stored in Capacitor: \( U = \frac{1}{2}CV^2 = \frac{Q^2}{2C} = \frac{1}{2}QV \)
Energy Density: \( u = \frac{1}{2}\varepsilon_0E^2 \)

3. Current Electricity

Electric Current: \( I = \frac{Q}{t} \)
Instantaneous Current: \( I = \frac{dQ}{dt} \)
Current Density: \( J = \frac{I}{A} \)
Drift Velocity: \( v_d = \frac{I}{neA} \)
Current in Terms of Drift Velocity: \( I = neAv_d \)
Ohm's Law: \( V = IR \)
Resistance: \( R = \rho\frac{l}{A} \)
Conductivity: \( \sigma = \frac{1}{\rho} \)
Temperature Dependence of Resistance: \( R_T = R_0[1+\alpha(T-T_0)] \)
Resistors in Series: \( R_{\text{eq}} = R_1+R_2+\cdots \)
Resistors in Parallel: \( \frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2} +\cdots \)
Electrical Power: \( P = VI = I^2R = \frac{V^2}{R} \)
Electrical Energy: \( W = VIt \)
Terminal Voltage of Cell: \( V = E-Ir \)
Kirchhoff's Junction Rule: \( \sum I = 0 \)
Kirchhoff's Loop Rule: \( \sum \Delta V = 0 \)
Wheatstone Bridge Condition: \( \frac{P}{Q} = \frac{R}{S} \)
Meter Bridge: \( \frac{R}{S} = \frac{l}{100-l} \)
Potentiometer Principle: \( V \propto l \)

4. Moving Charges and Magnetism

Lorentz Force: \( \vec{F} = q(\vec{E}+\vec{v}\times\vec{B}) \)
Magnetic Force on Moving Charge: \( F = qvB\sin\theta \)
Radius of Circular Path: \( r = \frac{mv}{qB} \)
Time Period of Charged Particle: \( T = \frac{2\pi m}{qB} \)
Cyclotron Frequency: \( f = \frac{qB}{2\pi m} \)
Biot-Savart Law: \( d\vec{B} = \frac{\mu_0}{4\pi} \frac{I\,d\vec{l}\times\hat{r}}{r^2} \)
Magnetic Field Due to Long Straight Wire: \( B = \frac{\mu_0I}{2\pi r} \)
Magnetic Field at Center of Circular Coil: \( B = \frac{\mu_0NI}{2R} \)
Ampere's Circuital Law: \( \oint\vec{B}\cdot d\vec{l} = \mu_0I \)
Magnetic Field Inside Solenoid: \( B = \mu_0nI \)
Force on Current Carrying Conductor: \( \vec{F} = I\vec{l}\times\vec{B} \)
Force Between Parallel Conductors: \( \frac{F}{l} = \frac{\mu_0I_1I_2}{2\pi d} \)
Torque on Current Loop: \( \tau = NIAB\sin\theta \)
Magnetic Dipole Moment: \( M = NIA \)
Moving Coil Galvanometer: \( I = \frac{k\theta}{NBA} \)

5. Magnetism and Matter

Magnetic Dipole Moment of Bar Magnet: \( M = m(2l) \)
Torque on Magnetic Dipole: \( \vec{\tau} = \vec{M}\times\vec{B} \)
Potential Energy of Magnetic Dipole: \( U = -\vec{M}\cdot\vec{B} \)
Magnetic Field on Axial Position: \( B = \frac{\mu_0}{4\pi} \frac{2M}{r^3} \)
Magnetic Field on Equatorial Position: \( B = \frac{\mu_0}{4\pi} \frac{M}{r^3} \)
Magnetic Intensity: \( H = \frac{B}{\mu_0}-M \)
Magnetic Susceptibility: \( \chi_m = \frac{M}{H} \)
Relative Permeability: \( \mu_r = 1+\chi_m \)

6. Electromagnetic Induction

Magnetic Flux: \( \Phi_B = BA\cos\theta \)
Faraday's Law: \( \varepsilon = -\frac{d\Phi_B}{dt} \)
Induced EMF in N Turns: \( \varepsilon = -N\frac{d\Phi_B}{dt} \)
Motional EMF: \( \varepsilon = Blv \)
Self Inductance: \( \Phi = LI \)
Self Induced EMF: \( \varepsilon = -L\frac{dI}{dt} \)
Mutual Inductance: \( \varepsilon_2 = -M\frac{dI_1}{dt} \)
Energy Stored in Inductor: \( U = \frac{1}{2}LI^2 \)

7. Alternating Current

Alternating Current: \( i = i_0\sin\omega t \)
Alternating Voltage: \( v = v_0\sin\omega t \)
RMS Current: \( I_{\text{rms}} = \frac{I_0}{\sqrt{2}} \)
RMS Voltage: \( V_{\text{rms}} = \frac{V_0}{\sqrt{2}} \)
Inductive Reactance: \( X_L = \omega L \)
Capacitive Reactance: \( X_C = \frac{1}{\omega C} \)
Impedance: \( Z = \sqrt{R^2+(X_L-X_C)^2} \)
AC Current: \( I = \frac{V}{Z} \)
Phase Angle: \( \tan\phi = \frac{X_L-X_C}{R} \)
Average Power: \( P = V_{\text{rms}}I_{\text{rms}}\cos\phi \)
Resonant Frequency: \( f_0 = \frac{1}{2\pi\sqrt{LC}} \)
Transformer Relation: \( \frac{V_s}{V_p} = \frac{N_s}{N_p} \)

8. Electromagnetic Waves

Speed of Electromagnetic Wave: \( c = \frac{1}{\sqrt{\mu_0\varepsilon_0}} \)
Wave Relation: \( c = \nu\lambda \)
Electric and Magnetic Fields Relation: \( E_0 = cB_0 \)
Electric Energy Density: \( u_E = \frac{1}{2}\varepsilon_0E^2 \)
Magnetic Energy Density: \( u_B = \frac{B^2}{2\mu_0} \)

9. Ray Optics and Optical Instruments

Law of Reflection: \( i = r \)
Snell's Law: \( n_1\sin i = n_2\sin r \)
Refractive Index: \( n = \frac{c}{v} \)
Critical Angle: \( \sin C = \frac{n_2}{n_1} \)
Mirror Formula: \( \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \)
Mirror Magnification: \( m = -\frac{v}{u} \)
Lens Formula: \( \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \)
Lens Magnification: \( m = \frac{v}{u} \)
Power of Lens: \( P = \frac{1}{f} \)
Lenses in Contact: \( P = P_1+P_2+\cdots \)
Lens Maker's Formula: \( \frac{1}{f} = (\mu-1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \)
Prism Formula at Minimum Deviation: \( \mu = \frac{\sin\left(\frac{A+\delta_m}{2}\right)} {\sin\left(\frac{A}{2}\right)} \)
Magnifying Power of Simple Microscope: \( M = 1+\frac{D}{f} \)
Magnifying Power of Astronomical Telescope: \( M = \frac{f_o}{f_e} \)

10. Wave Optics

Path Difference: \( \Delta x = d\sin\theta \)
Constructive Interference: \( \Delta x = n\lambda \)
Destructive Interference: \( \Delta x = (2n+1)\frac{\lambda}{2} \)
Young's Double Slit Fringe Width: \( \beta = \frac{\lambda D}{d} \)
Position of Bright Fringe: \( x_n = n\frac{\lambda D}{d} \)
Position of Dark Fringe: \( x_n = (2n-1)\frac{\lambda D}{2d} \)
Single Slit Diffraction Condition: \( a\sin\theta = n\lambda \)
Width of Central Maximum: \( W = \frac{2\lambda D}{a} \)
Malus's Law: \( I = I_0\cos^2\theta \)

11. Dual Nature of Radiation and Matter

Photon Energy: \( E = h\nu = \frac{hc}{\lambda} \)
Photon Momentum: \( p = \frac{h}{\lambda} \)
Einstein's Photoelectric Equation: \( h\nu = \phi + K_{\max} \)
Maximum Kinetic Energy: \( K_{\max} = \frac{1}{2}mv_{\max}^2 = eV_0 \)
Threshold Frequency: \( \nu_0 = \frac{\phi}{h} \)
de Broglie Wavelength: \( \lambda = \frac{h}{p} = \frac{h}{mv} \)
Wavelength of Electron Accelerated Through Potential V: \( \lambda = \frac{h}{\sqrt{2meV}} \)

12. Atoms

Bohr Radius: \( r_n = \frac{n^2h^2\varepsilon_0} {\pi me^2} \)
Radius of nth Orbit: \( r_n = n^2a_0 \)
Electron Velocity in nth Orbit: \( v_n \propto \frac{1}{n} \)
Energy of Electron: \( E_n = -\frac{13.6}{n^2}\text{ eV} \)
Angular Momentum: \( mvr = \frac{nh}{2\pi} \)
Rydberg Formula: \( \frac{1}{\lambda} = R \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \)

13. Nuclei

Nuclear Radius: \( R = R_0A^{1/3} \)
Mass Defect: \( \Delta m = Zm_p+(A-Z)m_n-M \)
Binding Energy: \( BE = \Delta mc^2 \)
Binding Energy per Nucleon: \( \frac{BE}{A} \)
Radioactive Decay Law: \( N = N_0e^{-\lambda t} \)
Activity: \( R = \lambda N \)
Half Life: \( T_{1/2} = \frac{0.693}{\lambda} \)
Mean Life: \( \tau = \frac{1}{\lambda} \)
Relation Between Mean Life and Half Life: \( \tau = \frac{T_{1/2}}{0.693} \)
Energy-Mass Relation: \( E = mc^2 \)

14. Semiconductor Electronics

Current: \( I = I_e+I_h \)
Conductivity: \( \sigma = ne\mu_e+ pe\mu_h \)
Resistivity: \( \rho = \frac{1}{\sigma} \)
Transistor Current Relation: \( I_E = I_B+I_C \)
Common Base Current Gain: \( \alpha = \frac{I_C}{I_E} \)
Common Emitter Current Gain: \( \beta = \frac{I_C}{I_B} \)
Relation Between Alpha and Beta: \( \beta = \frac{\alpha}{1-\alpha} \)
Relation Between Beta and Alpha: \( \alpha = \frac{\beta}{1+\beta} \)

Important:

Students should understand the meaning, application and limitations of each formula instead of only memorising them. Regular numerical practice and revision can improve Physics problem-solving skills.

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FORMULA'S PHYSICS