\(v = v_0 + at\)
i love this one!!! i use it when i'm trying to find the final velocity at the end of a trip. this one is very simple, but it doesn't tell us anything about position so it gets second place among the kinematics.
\(x = x_0 + v_0t + \frac {1}{2} at^2\)
this one is excellent. it covers all the bases, assuming that acceleration is constant. since acceleration is usually constant, this one is a win!!! it's also very helpful with free fall or projectile motion, since we know that a = 9.81, and the initial velocity is either give or 0.
\(v^2 = (v_0)^2 + 2a(x - x_0)\)
this one is good for when you are trying to find out the braking distance. at least, that's the only time i've ever used it. not a fan of this one othewise.
\(F = ma\)
ah yes. an all around classic. either the object is accelerating, and the
magnitude of the forces add up to some scalar, or the accleration is zero, and the
magnitudes of the forces all add up to zero. either way this one is very important and i love it.
\(F_{net} = F_1 + F_2 ... F_n\)
this is an extension of the previous equation. we know that the net force, which is a scalar, is the same as all of the other forces added up. if they don't all add up to zero that means that the object is accelerating.
\(f = \mu N\)
friction is in fact fun!!!! but not when i don't remember which normal force this equation is referring to. it's the one that's pushing upwards from the floor to the surface. this is
only for kinetic friction. in order to calculate static friciton, you must use newton's second law.
\(W = Fdcos \theta = \Delta KE\)
i like the energy part of this equation, but the \(Fdcos \theta\) part confuses me. what's theta?? is it x displacement or total displacement??? what's the force, net force??? ugh.
\(KE = \frac{1}{2}mv^2\)
i like this equation. \(\frac{1}{2}xy^2\) is such a real one in the world of physics, problably because it's the integral of x multiplied by some fundamental constant. who knows how it work?? not me.
\(U = mgh\)
this one is one of my favorites!!! it's so easy, and it makes perfect sense. potential energy is reliant on mass, gravity, and height. the energy equations are truly perfect.
\(F_{c} = \frac{mv^2}{r}\)
this one can be confusing but it's just important to remember that centripetal force is not actually a force, it's the sum of the forces in the centripetal direction. sometimes this is normal force, sometimes it's weight + normal force, sometimes it's friction, but \(F_{c}\) is not acutally something that goes in the force diagram.