Introduction to Motion

Review the whole scalar/vector business with every sunrise until the whole positive vs. negative acceleration thing makes sense. Also: notation, notation, notation. A vector such as velocity is or v. The magnitude of a vector such as velocity is |v|, which identical to the speed s in the case of velocity. The average speed (or average velocity, etc.) is either or s_avg, or in the case of vector form then v_avg.

Lastly, don’t forget the units. Or the hats. They both matter a whole lot in physics. A velocity of in the positive x-direction would be written more concisely as .

Free Fall and Projectile Motion

The signs are so, so important. One negative flipped to positive, and it’s all over for a sensible answer. Likewise, life depends on keeping track of the vectors and their components.

Forces: Newton’s Three Laws of Motion

Action-reaction force pairs are never the force of gravity countered by a normal force. The magnitudes may be the same, but that doesn’t make them an action-reaction pair. Only label forces acting on an object in its free-body diagram, and not the ones it exerts itself, such as its gravitation pull on Earth or its push on whatever surface it’s sitting on.

If it seems that a problem doesn’t have enough information to go on, start labeling everything given, and listing all equations relevant to the information available. For example, we can find acceleration from velocity and time, or distance and a pair of times. As long as acceleration’s constant, we can use any of the projectile equations.

Force of Gravity and Orbital Motion

Orbital motion doesn’t involve constant velocity because of the changing direction, but it does have constant speed. The force of gravity always pulls objects towards each other, because it’s attractive.

Unbalanced Forces

Always, no, never omit friction on a free-body diagram. If there’s acceleration and a contact force, by which we mean a normal force, there’s friction.

Be careful that the right kind of friction makes it into the diagram: “Static” for stationary, “kinetic” for movement.

Include every force acting on the object on the diagram. Separate out x- and y-forces. Balanced forces add to zero, while unbalanced forces equal .