Newton’s 1^st law of motion is often called the Law of Inertia. Inertia is a property of matter that opposes any change in motion.

Newton’s 1^st law can be stated as such: an object at rest will remain at rest, an object in motion will continue moving at a constant speed in a straight line [unless acted on by some unbalanced (net) force].   Newton’s 1^st law of motion describes what occurs when no unbalanced force acts on an object.

If the object is at rest to begin with, it will remain in static equilibrium. The study of bodies at rest is called statics. It is a subdivision of the larger category of dynamics, which is a subcategory of mechanics.

For an object to remain at rest or to continue its motion undisturbed, the sum of the forces acting on it must equal zero. Notice, it is not a requirement that NO forces be acting on it just that their sum = 0.

Σ F = 0

[NOTE: = Greek letter sigma represents the sum of]

Here is an example of a statics problem.

For the diagram below, construct a free body diagram that consists of W, T₁ and T₂. Assign an angle for T₁ with respect to the x-axis and an angle for T₂ with respect to the x-axis

Image from http://mypages.iit.edu/~smart/acadyear/statics.htm

 

For example purposes, let’s say that W = 500. N and that angle 1 is 30^o and angle 2 is 50^o. Solve for the values of T₁ and T₂.

Because the system is at rest (or moving with constant velocity), the system is in equilibrium.

Therefore F_netx = 0 and Right Forces = Left Forces

T₁ cos 30 = T₂ cos 50; 0.866 T₁ = 0.643 T₂; T₁ = 0.742 T₂

 

This is the best that it gets for the x-axis since there are two unknowns. Luckily, we have the y-axis to use for our second equation.

F_nety = 0 and Top Forces = Bottom Forces

T₁ sin 30 + T₂ sin 50 = W sin 90

0.500 T₁ + 0.766 T₂ = 500. N (Eq 1)

Substitution of T₁ = 0.742 T₂ into the equation yields…

0.500 (0.742 T₂) + 0.766 T₂ = 500. N

0.371 T₂ + 0.766 T₂ = 500. N

1.137 T₂ = 500. N

T₂ = 440. N

Substitution into (Eq 1) yields ..

T₁ = 440N (0.742) = 326 N

 Notice that because T₂ has a greater vertical component, it supports more of the weight. The x-component of a tension force is wasted when supporting a vertical weight!

 

(source)