3.2 Significant figures Measurements are not infinitely precise. For example, if you measure something with a ruler that has markings every eighth of an inch, and the measurement lies between two markings, you need to estimate the length. If you Continue Reading
11.5 Equilibrium revisited An object is in static equilibrium when the following conditions are true: The net torque acting on the object is zero: $$\tau_\textit{net} = 0$$ The net force acting on the object is zero: $$\vec{F}_\textit{net} = 0$$ Remember Continue Reading
6.7 Conservation of energy revisited Energy is not created or destroyed. The statement is an expression of conservation of energy; we account for all energy transfers between kinetic and potential energy within a system, and any energy that is “lost” Continue Reading
2.2 Representation Visually, vectors are represented as arrows such as in the figure below. Symbolically, a vector is notated with an arrow on top of it when hand-written. The symbol \(\vec{A}\) would be read as “vector A.” When typed, we Continue Reading
1.2 Inverse trig functions An inverse function can be thought of as a function that “undoes” another function. For example, subtraction undoes addition: and division undoes multiplication: In the same way, there are inverse trig functions.* They are called inverse Continue Reading
A.4: Solving systems of two equations Another situation that comes up in physics is where something is described by a system of multiple equations and variables. As long as there are the same number of equations as unknowns, you can Continue Reading
A.3: Solving quadratic equations All the examples so far have been linear equations: none of the unknowns were raised to any power*. In physics, there are often situations described by quadratic equations, where some unknown quantity is squared. When the Continue Reading
A.2: Basic algebra The field of algebra gives us the basic tools we need to manipulate equations, or to pull useful information out of a mathematical sentence. There is one all-encompassing rule that must be obeyed: Whatever you do on Continue Reading
A.1: Math is a way of writing language Just like we use a spoken and written language such as English, Spanish, or Chinese to communicate verbally, we use mathematics to communicate ideas in science. Mathematical notation has been developed to Continue Reading
12.2 2D Kinematics & Projectile motion A projectile is any object that is thrown or launched. As with 1D kinematics problems, we’re not concerned with what caused the object to be launched, or how it was launched in the first Continue Reading