Net Force and Newton’s Laws of Motion
A free preview from The Ultimate Crash Course for STEM Majors by Jonathan David.
Resultant Force
$$
R_x = F_{x,1} + F_{x,2} + F_{x,3} + \cdots
= \sum_i F_{x,i}
$$
$$
R_y = F_{y,1} + F_{y,2} + F_{y,3} + \cdots
= \sum_i F_{y,i}
$$
$$
\vec{R} = \vec{F}_1 + \vec{F}_2 + \vec{F}_3 + \cdots
= \sum_i \vec{F}_i
$$
$$
|\vec{R}| = F
= \sqrt{R_x^2 + R_y^2}
= \sqrt{
\left(\sum_i F_{x,i}\right)^2
+
\left(\sum_i F_{y,i}\right)^2
}
$$
Newton’s First Law of Motion
When the net force on a body is zero, its velocity remains constant and its acceleration is zero. A body at rest remains at rest, and a moving body continues moving at constant velocity.
The Newton — Unit of Force
Force is measured in newtons, abbreviated $\mathrm{N}$. One newton is the force required to accelerate a mass of one kilogram at one meter per second squared.
$$ 1\,\mathrm{N} = 1\,\mathrm{kg}\cdot\frac{\mathrm{m}}{\mathrm{s}^2} $$Force equals mass times acceleration.
Newton’s Second Law of Motion
When a nonzero net force acts on a body, the body accelerates in the direction of the net force. For constant mass:
$$ \sum_i \vec{F}_i = m\vec{a} $$Formulas
| Quantity or Law | Formula |
|---|---|
| Weight |
$w = mg$ — mass times gravitational acceleration.
Vector form: $\vec{w} = m\vec{g}$. |
| Newton’s Third Law — Action and Reaction |
$\vec{F}_{1,2} = -\vec{F}_{2,1}$
The forces are equal in magnitude, opposite in direction, and act on different bodies. |
