The following relationships are used in problems involving balanced and unbalanced forces (including friction and tension), mass, acceleration, and gravitational field strength.

$$ F=ma $$

$$ W=mg $$

Energy can be neither created nor destroyed only converted from one form to another → This is a statement of the principle of conservation of energy. A conclusion of this principle is that the total energy in a closed system remains constant.

Using this principles and the following relationships problems involving work done, potential energy, kinetic energy, and power can be solved.

$$ E_w=Fd $$

$$ E_p=mgh $$

$$ E_k=\dfrac{1}{2}mv^2 $$

$$ P=\dfrac{E}{t} $$

Vectors can be added by drawing tip-to-tail diagrams and then calculating the resultant vector using $SOH \space CAH \space TOA$ or the cosine and sine rule. However for vectors not at right angles to each other, it is often easier to add them by splitting them into components and then calculating the resultant vector from its components.

To resolve a vector into two perpendicular components $SOH \space CAH \space TOA$ can be used.

Free body diagrams are diagrams which show all the forces acting on an object. In a free body diagram, arrows are used to represent forces — they must be labelled with what force they are showing and the relative lengths of the arrows must be accurate to show which forces are bigger or smaller or the same.