Kinematics (Quantitative Description of Motion)
| Formula | Definition and explanations |
|---|---|
| \( s_{av} = \dfrac{d}{\Delta t} \) | sav is the average speed (scalar) d is the distance Δ t is the time elapsed |
| \( v_{av} = \dfrac{x_f - x_i}{t_f - t_i} =\dfrac{\Delta x}{\Delta t} \) | vav is the average velocity (vector) Δ x is the displacement(vector) Δ t is the time elapsed |
| \( a_{av} = \dfrac{v_f - v_i}{t_f - t_i} =\dfrac{\Delta v}{\Delta t} \) | aav is the average acceleartion (vector) Δ v is the change in velocity (vector) Δ t is the time elapsed |
| \( v_{av} = \dfrac{v_i + v_f}{2} \) | vav is the average velocity (vector) vi is the initial velocity (vector) vf is the final velocity (vector) |
| \( v_{f} = v_{i} + a \Delta t \) | vf is the final velocity (vector) vi is the initial velocity (vector) a is the acceleration (vector) |
| \( \Delta x = v_i \Delta t + \dfrac{1}{2} a (\Delta t)^2 \) | Δ x is the displacement (vector) vi is the initial velocity (vector) a is the acceleration (vector) |
| \( \Delta x = v_f \Delta t - \dfrac{1}{2} a (\Delta t)^2 \) | Δ x is the displacement (vector) vf is the final velocity (vector) a is the acceleration (vector) |
| \( \Delta x = \dfrac{v_f+v_i}{2} \Delta t \) | Δ x is the displacement (vector) vf is the final velocity (vector) vi is the initial velocity (vector) |
| \( v^2_f = v^2_i + 2 a \cdot \Delta x \) | vf is the final velocity (vector) vi is the initial velocity (vector) Δ x is the displacement (vector) a is the acceleration (vector) |
Relative Velocity
| Formula | Definition and explanations |
|---|---|
| \( v_{AC} = v_{AB}+v_{BC} \) | vAC is the velocity of A with respect to C (vector) vAB is the velocity of A with respect to B (vector) vBC is the velocity of B with respect to C (vector) |
Kinematics (Quantitative Description of Projectile Motion)
| Formula | Definition and explanations |
|---|---|
| \( v_{ix} = |v_i|\cos(\theta) \\ v_{iy} = |v_i|\sin(\theta) \) | vi is the initial velocity (vector) vix is the component of the initial velocity along the horizontal direction x (scalar) viy is the component of the initial velocity along the vertical direction y (scalar) θ is the initial angle that vi makes with the horizontal. |
| \( \Delta x = |v_i|\cos(\theta) \Delta t \) | Δx is the displacement along the horizontal direction x |
| \( \Delta y = |v_i| \sin(\theta) \Delta t - \dfrac{1}{2} g (\Delta t)^2 \) | Δy is the displacement along the vertical direction y |
| \( R = \dfrac{v^2_i \sin(2\theta)}{g}\) | R is the range or horizontal distance travelled when the projectile hits the ground |
| \( T = \dfrac{2 v_i \sin(\theta)}{g}\) | T is total time to hit the ground |
| \( H = \dfrac{v^2_i \sin^2(\theta)}{2 g}\) | H maximum height reached above the ground g = 9.8 m / s2 |
Dynamics (Forces and Momentum)
| Formula | Definition and explanations |
|---|---|
| \( F = m a \) | F is the net force (vector) m is the mass a is the acceleration (vector) |
| \( F_g = m g \) | Fg is the weight (vector) m is the mass g is the acceleration (near the Earth) due to gravitation (vector) |
| \( | F_f | = \mu | F_N | \) | Ff is the force of friction (vector) μ is the coefficient of friction (μ may be μk kinetic coefficient or μs static coefficient of friction) FN is the normal (to the surface) force (vector) |
| \( p = m v \) | p is the momentum (vector) m is the mass v is the velocity (vector) |
| \( \Delta p = F \Delta t \) | Δ p is the change in momentum (vector) F is the applied force (vector) Δ t is the elapsed time (F Δ t) is called impulse (vector) |
Circular Motion
| Formula | Definition and explanations |
|---|---|
| \( a_c = \dfrac{v^2}{r} \) | ac is the centripetal acceleration v is the velocity r is the radius |
| \( F_c = \dfrac{m v^2}{r} \) | Fc is the centripetal force v is the velocity m is the mass r is the radius |
| \( v = \dfrac{2 \pi r}{T} \) | v is the velocity r is the radius T is the period (time for one complete revolution) |
Work, Potential and Kinetic Energies
| Formula | Definition and explanations |
|---|---|
| \( W = F d \cos(\theta) \) | W is the work done by the force F F is the applied force (constant) d is the distance θ is the angle between F and the direction of motion |
| \( E_k = \dfrac{1}{2} m v^2 \) | Ek is the kinetic energy v is the velocity m is the mass |
| \( E_p = m g h \) | Ep is the potential energy of an object close to the surface of Earth m is the mass of the object h is the height of the object with respect to some refernce (ground for example) g = 9.8 m/s2 |
| \( E_t = E_k + E_p \) | Et is the total energy Ek is the kinetic energy Ep is the potential energy |
Springs, Hooke's Law and Potential Energy
| Formula | Definition and explanations |
|---|---|
| \( F_s = k x \) | F is the force applied to compress or stretch a spring k is the spring constant x is the length of extension or compression of the spring |
| \( E_s = \dfrac{1}{2} k x^2 \) | Es is the potential energy stored in a spring when compressed or extended k is the spring constant x is the length of extension or compression of the spring |
Period of Simple Harmonic Motions
| Formula | Definition and explanations |
|---|---|
| \( T_s = 2\pi \sqrt{\dfrac{m}{k}} \) | Ts is the time period of motion k is the spring constant m is the mass attached to the spring |
| \( T_p = 2\pi \sqrt{\dfrac{L}{g}} \) | Ep is the time period of motion L is the length of the pendilum g is the acceleration due to gravity |
Gravitational Fields and Forces
| Formula | Definition and explanations |
|---|---|
| \( F = G \dfrac{m_1 m_2}{r^2} \) | F is force of attraction G is the universal gravitational constant m1 and m1 are the masses of the two objects attracting each other r is the distance separating the centers of the two objects |
| \( g_r = \dfrac{G m}{r^2} \) | gr gravitational field intensity at a distance r G is the universal gravitational constant m is the mass r is the distance (from mass m) where the field is measured |
| \( E_p = -\dfrac{G M m}{r} \) | Ep gravitational potential energy of mass m G is the universal gravitational constant G is the mass of the attracting body m is the mass being attracted r is the distance separating the centers of the masses M and m |
Satelite motion, orbital speed, period and radius
| Formula | Definition and explanations |
|---|---|
| \( v = \sqrt{ \dfrac{G M}{r} } \) | v is the orbital speed of the satellite G is the universal gravitational constant M is the mass of the attracting body (Earth for example) r is the distance from the center of mass M to the position of the satellite |
| \( T = \sqrt{ \dfrac{4\pi^2r^3}{G M} } \) | T is the orbital period of the satellite G is the universal gravitational constant m is the mass r is the distance from the center of mass M to the the position of the satellite |
| \( v = \dfrac{2\pi r }{T} \) | v is the orbital speed of the satellite r is the distance from the center of mass M to the the position of the satellite T is the orbital period of the satellite |
Electric forces, fields and potentials
| Formula | Definition and explanations |
|---|---|
| \( F = k \dfrac{q_1 q_2}{r^2} \) | F is the electric force k is a constant q1 and q1 are the charges attracting or repulsing each other r is the distance separating the two charges |
| \( F = q E \) | F is the electric force q is the charge E is the eletcric field |
| \( E = k \dfrac{q}{r^2} \) | E is the electric field due charge q k is a constant q is the charge r is the distance from the charge q where E is being calculated |
| \( E_p = k \dfrac{q_1 q_2}{r} \) | Ep is the electric potential energy for a system of two charges k is a constant q1 and q1 are the charges r is the distance separating the two charges |
| \( V = k \dfrac{q}{r} \) | V is the electric potential k is a constant q is the charge r is the distance from the charge q |
| \( E = \dfrac{V}{d} \) | E is the electric field between two large, oppositely charged, conducting parallel plates V is the electric potential difference between the plates d is the distance separating the two plates |
Magnetic fields and forces
| Formula | Definition and explanations |
|---|---|
| \( B = \dfrac{\mu _0 I}{2 \pi r} \) | B is magnetic field due to current I in a long conductor of length L μ0 is permeability in vacuum I the current in the conductor L is the length of the conductor r is the distance from the conductor to where the field B is calculated |
| \( B = \dfrac{\mu _0 N I}{L} \) | B is the magnetic field (in the center of the solenoid) due to current I in a solenoid of length L μ0 is permeability in vacuum I the current in the solenoid L is the length of the solenoid N is the number of turns of the solenoid |
| \( F_m = q v B \sin(\theta) \) | Fm is the magnetic force (due to B) on a charge q moving at a velocity v B the magnetic field θ is the angle between B and the direction of motion of q |
| \( F_m = I L B \sin(\theta) \) | Fm is the magnetic force (due to B) on a wire with current I and length L B the magnetic field θ is the angle between B and the wire |
| \( F_m = \dfrac{ \mu _0 I_1 I_2 L }{2 \pi r} \) | Fm is the magnetic force of attraction or repulsion between two parallel wires μ0 is permeability in vacuum I1 and I2 are the currents in the two wires L is the common length between the two wires |
Waves
| Formula | Definition and explanations |
|---|---|
| \( v = \lambda f \) | v is the wave velocity λ is the wavelength f is the frequency |
| \( f = \dfrac{1}{T} \) | f is the wave frequency T is the period of the wave |
Optics
| Formula | Definition and explanations |
|---|---|
| \( v = \dfrac{c}{n} \) | v is the velocity of light in a medium of index n c is speed of light in vacuum ( = 3.0 × 108m/s) n is the index of refraction of the medium |
| \( n_1 \sin \theta_1 = n_2 \sin \theta_2 \) | n1 is the index of refraction of medium 1 n2 is the index of refraction of medium 2 θ1 is the angle of incidence in medium 1 θ2 is the angle of refraction in medium 2 |
| \( \theta_c = \sin^{-1}(\dfrac{n_2}{n_1}) \) | θc is the critical angle such that when the angle of incidence is bigger that θc all light is reflected to medium 1 n1 is the index of refraction of medium 1 (medium of incidence) n2 is the index of refraction of medium 2 (medium of refraction) |
| \( \dfrac{1}{D_0} + \dfrac{1}{D_i} = \dfrac{1}{F} \) | D0 is the distance to the object Di is the distance to the image F is the focal length |
Photoelectric Effects
| Formula | Definition and explanations |
|---|---|
| \( E = h f \) | E is the energy of the photon h is Plank's constant f is the wave frequency of the photon |
| \( E_k = h f - \phi \) | Ek is the kinetic energy h is Plank's constant f is the wave frequency of the photon φ is the work function of the metal (minimum work required to extract an electron) |
| \( p = \dfrac{h}{\lambda} \) | p is the momentum of the photon h is Plank's constant λ is the photon wavelength |
DC Circuits
| Formula | Definition and explanations |
|---|---|
| \( V = R I \) | V is the voltage across a resistor R is the resistance of the resistor I is the current through the resistor |
| \( P = I^2 R = \dfrac{V^2}{R} = I V \) | P is the power dissipated as heat into a resistor I is current through the resistor R is the resistance of the resistor V is the voltage across the resistor |
| \( R_s = R_1 + R_2+... \) | Rs is the total resistance equivalent to several resistors in series (end to end) R1 resistance of resistor 1 R2 resistance of resistor 2 |
| \( \dfrac{1}{R_p} = \dfrac{1}{R_1} + \dfrac{1}{R_2} ... \) | Rp is the total resistance equivalent to several resistors in parallel (side by side) R1 resistance of resistor 1 R2 resistance of resistor 2 |
| \( C = \dfrac{\epsilon A}{d} \) | C is the capacitance of a capacitor made up of two parallel plates ε is the permittivity of the dielectric inside the two plates A is the common area of the two plates d is the distance between the two plates |
| \( Q = C V \) | Q is the total charge in a capacitor made up of two parallel plates C is the capacitance V is the voltage across the capacitor |
| \( W = \dfrac{C V^2}{2} \) | W is the total energy stored in a capacitor C is the capacitance V is the voltage across the capacitor |
