# Newton’s 1st Law of Motion

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

Newton’s 1st 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 1st 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 For example purposes, let’s say that W = 500. N and that angle 1 is 30o and angle 2 is 50o. 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 Fnetx = 0 and Right Forces = Left Forces

T1 cos 30 = T2 cos 50; 0.866 T1 = 0.643 T2T1 = 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.

Fnety = 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!

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