Idea: Newton's Laws

In an inertial reference frame, an object’s acceleration is zero if and only if the net external force acting on the object is zero.
$F=ma$, basically. We’ll discuss some subtleties in 3 weeks time.
For every force between two objects, there is a force that is equal in magnitude and opposite in direction.

Here are some common forces that you'll encounter throughout your studies:

Gravity. In most cases, gravity is a downward force given by mass times the gravitational constant $g = 9.8\,\unit{m/s^2}$. Later in the course we'll encounter the cases where distances get large enough such that this formula doesn't apply.
Normal Force. The normal force points perpendicular to a surface and takes on the value such that an object doesn't plow through the surface. A trick used in some problems is that when an object loses contact with the ground, the normal force is $0$. The normal force is also what a scale reads.
Friction. There are two kinds of friction, static and kinetic. Kinetic is simpler; when an two objects have a non-zero relative velocity with respect to each other there is a resistive force given by $F_k = \mu_k N$. Static is a bit subtler. When two objects hvae zero relative velocity with respect to each other, there can be a resistive force which is at most $F_s \le \mu_s N$. The object slips when the friction has to exceed this value.
Tension. Tension acts through a medium such as a rope. It pulls in on both ends with the same magnitude.
Spring Force. Springs apply a tension (or compression, which is negative tension!) which varies with how much it is stretched.

Tip: Free Body Diagrams

How do you keep track all of these forces in a complicated system? Draw a diagram! In competition, if you have time, draw a large one to make everything as clear as possible.

Idea: Centripetal Force

The NET force on a mass $m$ moving with velocity $v$ in a circle of radius $R$ is given by:$$F_c = \frac{mv^2}{R} = ma_c, \quad a_c = \frac{v^2}{R}.$$
The force points perpendicular to the mass’s velocity

Warning: Centripetal Force

The centripetal force is not an applied force that contributes to the net force! It's merely the requisite net force for an object to move in a circle. A common mistake is to add on the centripetal force to the existing forces that actual add up to the centripetal force.