Kinematics




∆x = 1/2 a*t^2 + Vi * t
Displacement is equal to half of the acceleration multiplied by time squared plus the initial velocity multiplied by time. In problems with no acceleration, like when solving in the x direction in projectile problems, the equation can be shortened tox=Vi * t because "a" is zero.

Vf^2 = Vi^2 + 2a∆x
The final velocity squared is equal to the initial velocity squared plus two times the acceleration multiplied by the displacement. This equation does not work if the final or initial velocity is zero.

Vf = Vi + a*t
You use this equation if you have the time and not the displacement, or if you need to know the time. The final velocity is equal to the initial velocity plus acceleration multiplied by time.

V =∆x/∆t
Velocity is equal to the displacement (m) divided by the time (s)

Dynamics



Fnet = m*a
Newton's Second Law, explaining that the total amount of force on an object is equal to an object's mass multiplied by it's acceleration. If the problem involves projectiles, the acceleration is either 9.8 or 10 meters per second squared, depending on how precise you need to be.

Fg = m*g
This equation is used to find the force of gravity of an object on Earth. To find the force, you multiply the object's mass (in kg) by gravity, which in free fall is -9.8.

Ffk ≤ µk*Fn
This equation is mainly used to find the kinetic friction of a system. You can also use simple algebra to work backwards and solve for Fn. The kinetic friction cannot be greater than the kinetic coefficient multiplied by the normal force, but they can be equal.

Ffs =µs*Fn
This equation is used to find the static coefficient of friction. This is much like the equation above it, but the static friction must be equal to Fn.

Centripetal Force


V = (2πr)/t
The velocity is equal to the circle's circumference divided by time.

T= 2πr/v
This is like the one above, but switched so if you already know the velocity, you can find the time.

Ac = v^2/r
The centripetal acceleration is equal to velocity squared divided by the radius.

Fc = m v^2/r
The centripetal force is equal to the mass times the velocity squared divided by the radius.

Fg = G (m1 * m2/r^2)
This is the Universal Gravitation equation. If the mass increases, so will the gravitational pull. As the radius between the two objects increases, the gravitational pull will lessen because the objects are farther apart. A common error when using this formula is forgetting to square the radius. This equation is used like Fg = m*g, but can be used anywhere, which is helpful when trying to find the force of gravity of objects in space.

Energy




Eel = 1/2k∆x^2
The elastic energy in an object is equal to half of its spring constant times its displacement squared.

F = k∆x
This equation is known as Hooke's Law. In this equation, F = force, k = spring constant (the slope of a f vs ∆x graph), and ∆x is the displacement.

Eg = mgh
The gravitational energy is equal to the mass multiplied by gravity, multiplied by height.

Ek = 1/2 m*v^2
The Kinetic Energy (energy an object has while moving) is equal to half of its mass times velocity squared.

W + Q + R = ∆E
This is the First Law of Thermodynamics, and means that working + heating + radiating = the displacement of energy (Ek + Eel +Eg + ...) It is also known as the Law of Conservation of Energy. Working is defined as the mechanical transfer of energy. Often in beginner's physics , Q and R can be set to zero to make the calculations easier, making the equation W = ∆E

W=F||∆x
This is another equation to find the work, which is equal to the force that is parallel to the object's displacement on a force diagram. This equation is useful when one does not know the amount of energy in a system, but still needs to find the work.

P = W/∆t
Power is equal to the work divided by time; the rate of work. Power is measured in Watts. Another equation that will give you the same answer is Power = force*velocity

Momentum




p = m*v
Momentum (p) is equal to the object's mass multiplied by its velocity.

Δp=pf-pi

This equation uses both the final momentum and the initial momentum to figure out the total impulse, or change in momentum, of the object.


J =∆p
The impulse (J) is equal to the change in momentum, which is ∆p, or the final momentum minus the initial momentum.

Fnet = ∆p/∆t
This equation is the same as Newton's Second Law, because you can substitute ∆p for m∆v, which would be divided by ∆t. m*∆v/∆t = m*a, therefore, Fnet = ∆p/∆t = m*a

Eki = Ekf
Perfect elastic collision, the system's initial kinectic energy is equal to the system's final kinetic energy.

(m1*Vi) + (m2*Vi) =(m1*Vf) + (m2*Vf)
Equation for a perfect elastic collision, where Eki=Ekf. This equation means that mass "n" times n's initial velocity plus mass x times x's initial velocity is equal to mass n times n's final velocity times mass x times x's final velocity.

m1 * v1 + m2 * v2

(m1 + m2) * v3= Equation for an inelastic collision, which is when the objects stick together. both of the object's momentum (m*v) is equal to the mass of the final object (the two stuck together) multiplied by it's new velocity.

Eki > Ekf
Inelastic collision equation, stating that the system's initial kinetic energy is greater than it's final kinetic energy

Electricity



Fe = K*(q1*q2/r^2)
This is much like the equation for universal gravitation, except the variables are changed. The force of electricity is equal to the electric constant "K" multiplied by the two object's charges and divided by the radius squared.



Variables




a = Acceleration (m/s/s)

ac = Centripetal acceleration, v^2/r

Eel = Elastic energy (springs, rubber bands, bungee cords)

Eg = Gravitational energy, an objects potential to fall

Eint = Internal energy, creates heat, often times caused by friction

Ek = Kinetic energy, when an object is moving

Et= The total amount of energy in an object

∆E = Ek + Eint + Eg +...

F = Force

Fe= Electric force. Very strong force that can cause objects to repel or attract.

Ff = Force of friction
  • Ffk ≤ µk*Fn
  • Ffs = µs*Fn

Fg = Force of gravity. On earth, Fg = mg, or you could use the universal gravitation equation for places other than Earth

Fn = Normal force i.e the floor pushing up on an object

Fnet = All of the forces acting on an object (F1 + F2 + F3 + ...) Fnet = ma

Ft= Tension force i.e. a rope pulling a box

G = Gravitational constant, 6.67 * 10^-11, used for objects not on Earth

g = Gravity, free fall is equal to -9.8m/s

h = Height

J = Joules, the measurement of energy

J = Impulse, the change in momentum

K = Electric constant

k = Spring constant, how stiff an object is. K = force/displacement, and is represented as the slope of an f vs ∆x graph

m = Mass, always use Kilograms

N = Newton, the measurement of force

P = Power, rate of working

p = Momentum, measured in kilogram-meters per second, kgm/s. Momentum is a vector, which means it has direction, and also a conserved property, which means there is a finite amount and it cannot be gained or lost in a closed system, much like energy.

Q = Heating, when an object gets heat from an outside force, such as a Bunsen burner

q = Charge, positive or negative

R = Radiating

T = The time it takes for an object to make a complete cycle, in seconds

V = Velocity

Vi = Initial velocity, the object's velocity when the experiment starts

Vf = Final velocity, the velocity of an object at the end of an experiment

W = Working, the mechanical transfer of energy

∆x = Position, also known as displacement. If an object moves forward three meters, then its displacement is three meters. if an objects moves forward three meters, and then backwards three meters (ending at the same place it started), then it has no displacement.

µk = The kinetic coefficient of friction, normally a decimal less than one. This coefficient is used when an object is moving.

µs = The static coefficient of friction, the force needed to move an object from rest. This number is often larger than the kinetic because it takes more force to move a resting object since the object has inertia.