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1. Newton’s Laws of Motion

First Law (Law of Inertia):
Formula:

$F_{text{net}} = 0$
Explanation: An object will stay at rest or in uniform motion unless acted upon by a force.

Second Law (Force and Acceleration):
Formula:

$F = ma$
Explanation: The force on an object is equal to its mass times its acceleration.

Third Law (Action and Reaction):
Formula:

$F_{text{action}} = -F_{text{reaction}}$
Explanation: For every action, there is an equal and opposite reaction.

2. Work, Energy, and Power

Work Done by a Force:
Formula:

$W = F cdot d cdot cos(theta)$
Explanation: Work is done when a force acts over a distance.

$F$is the force,

$d$is the distance, and

$theta$is the angle between the force and the direction of motion.

Kinetic Energy:
Formula:

$KE = frac{1}{2} mv^2$
Explanation: The energy an object has due to its motion, where

$m$is mass and

$v$is velocity.

Potential Energy:
Formula:

$PE = mgh$
Explanation: The energy stored in an object due to its height above the ground, where

$m$is mass,

$g$is acceleration due to gravity, and

$h$is height.

Power:
Formula:

$P = frac{W}{t}$
Explanation: Power is the rate at which work is done, where

$W$is work and

$t$is time.

3. Motion Equations (Kinematics)

Equation 1 (Displacement with constant acceleration):
Formula:

$v = u + at$
Explanation: Final velocity

$v$is initial velocity

$u$, plus acceleration

$a$times time

$t$.

Equation 2 (Displacement without final velocity):
Formula:

$s = ut + frac{1}{2} a t^2$
Explanation: Displacement

$s$is initial velocity

$u$times time

$t$, plus half the acceleration

$a$times time squared.

Equation 3 (Displacement with velocity):
Formula:

$s = left( frac{u + v}{2} right) cdot t$
Explanation: Displacement

$s$is the average of initial velocity

$u$and final velocity

$v$, times time

$t$.

4. Circular Motion

Centripetal Force:
Formula:

$F_c = frac{mv^2}{r}$
Explanation: The force that keeps an object moving in a circle, where

$m$is mass,

$v$is velocity, and

$r$is the radius of the circle.

Centripetal Acceleration:
Formula:

$a_c = frac{v^2}{r}$
Explanation: The acceleration that keeps an object moving in a circle.

5. Gravitation

Gravitational Force (Newton’s Law of Universal Gravitation):
Formula:

$F = frac{G m_1 m_2}{r^2}$
Explanation: The force between two masses

$m_1$and

$m_2$, separated by distance

$r$, where

$G$is the gravitational constant.

Gravitational Potential Energy:
Formula:

$PE = -frac{G m_1 m_2}{r}$
Explanation: The energy stored due to gravitational attraction between two masses.

6. Waves and Sound

Wave Speed:
Formula:

$v = f lambda$
Explanation: The speed

$v$of a wave is the frequency

$f$times the wavelength

$lambda$.

Sound Intensity:
Formula:

$I = frac{P}{A}$
Explanation: The intensity

$I$of sound is the power

$P$divided by the area

$A$through which the sound passes.

7. Thermodynamics

First Law of Thermodynamics (Energy Conservation):
Formula:

$Delta U = Q – W$
Explanation: The change in internal energy

$Delta U$of a system is equal to heat added

$Q$minus work done

$W$by the system.

Heat Transfer:
Formula:

$Q = mc Delta T$
Explanation: The heat

$Q$needed to change the temperature of a substance is its mass

$m$times its specific heat

$c$times the change in temperature

$Delta T$.

8. Electricity and Magnetism

Ohm’s Law:
Formula:

$V = IR$
Explanation: Voltage

$V$is current

$I$times resistance

$R$.

Coulomb’s Law (Electric Force):
Formula:

$F = frac{k_e q_1 q_2}{r^2}$
Explanation: The force between two charges

$q_1$and

$q_2$, separated by distance

$r$, where

$k_e$is Coulomb’s constant.

Electric Power:
Formula:

$P = IV$
Explanation: The power

$P$in an electrical circuit is the product of current

$I$and voltage

$V$.

9. Optics

Lens Equation:
Formula:

$frac{1}{f} = frac{1}{d_o} + frac{1}{d_i}$
Explanation: The inverse of the focal length

$f$of a lens is the sum of the inverses of the object distance

$d_o$and the image distance

$d_i$.

Magnification:
Formula:

$M = frac{h_i}{h_o} = frac{d_i}{d_o}$
Explanation: Magnification

$M$is the ratio of image height

$h_i$to object height

$h_o$, or the ratio of image distance

$d_i$to object distance

$d_o$.

10. Modern Physics

Einstein’s Mass-Energy Equation:
Formula:

$E = mc^2$
Explanation: Energy

$E$is equal to mass

$m$times the speed of light

$c$squared.

Photoelectric Effect (Energy of Photon):
Formula:

$E = hf$
Explanation: The energy

$E$of a photon is the frequency

$f$times Planck’s constant

$h$.