Newton's Laws of Motion

Previous: Motion in 2D and 3D

Newton's Laws of Motion is the fourth lecture in the Mechanics section of PH1011. It covers Newton's Laws and the set up of free body diagrams.

Next: Friction

Newton's Laws
(See Concepts)
 * 1st Law: v = constant <=> F = 0; an object's velocity will remain constant in the absence of external forces.
 * 2nd Law: F = ma; a net force will cause acceleration in that direction, and the acceleration will be inversely proportional to the object's mass.
 * 3rd Law: FA->B = -FB->A; every action has an equal and opposite reaction. The force exerted on one body by another will be matched by the force of the second body on the first.

Newton's Laws are only valid in inertial reference frames.

Free-body Diagrams
Free body diagrams are those in which only a point mass and its associated forces are considered. The point mass is represented as a dot and the forces are represented as arrows pointing away from it, labelled with the force's symbol and what it acts to and from (eg nS->B; the normal force of a surface acts upon a box, B). Various common forces are the weight (Earth -> Object), normal (surface -> Object, in a perpendicular direction to the surface plane and with equal magnitute to the relevant component of weight), tension (rope -> object, caused by pulling an object via rope), and friction (surface -> box again, acting along the surface).

Examples
This is most commonly seen as a mass sliding down a frictionless surface; the only forces in play are weight and the normal, which must be found using trigonometry to calculate their values from a known angle of slope.

It is also often used in examples with masses moving over a pulley; the pulley is assumed to be without mass or friction, and its string inextensible and massless. Two separate free body diagrams must be drawn; one per mass. Taking different direction for the y axis of the masses allows both accelerations to be equal, and therefore the string tension to be the same as well. These two resulting equations can be used to calculate the unknown quantities, and also show that the string tension is only equal to the total mass x gravity when the masses are equal.

Summary
Newton's Laws state that objects won't change velocity without external force, will accelerate with external force and will react equally when acted upon. Free body diagrams must have a point mass and its relevant forces, and are the easiest way of making calculations simply.