Newton's First and Second Laws of Motion, Mass, Weight

Newton's first law of motion

Newton's first law of motion, also known as the law of inertia, states that an object at rest will remain at rest, and an object in motion will remain in motion, unless acted upon by an unbalanced force. In other words, an object will stay still or keep moving at the same speed and in the same direction unless a non-zero net force acts on it.

Newton's second law of motion

Newton's second law is one of the most important equations in physics and the first bridge we have been learning between kinematics (how things move) and mechanics (how energy and forces affect motion). It states that force is proportional to acceleration, with mass as the coefficient:

$$\vec{F}_{net}=\sum\limits_i\vec{F_i}=m\vec{a}$$

where $\vec{F}_{net}$ is the net force on an object, $m$ is the mass of the object, and $\vec{a}$ is the acceleration of the object.

This equation can also be projected: $\vec{F}_x=m\vec{a}_x$, where $x$ is any direction, such as the horizontal direction.

Mass and weight

In physics, mass is the quantity of matter in a physical body, with the SI base unit of kilogram. Weight is the magnitude of the gravitational force acting on a physical body, with the unit of newton. Based on Newton's second law, mass and weight are connected through an acceleration $\vec{g}$, called the gravitational acceleration:

$$\vec{F}_g=m\vec{g}\qquad W=||\vec{F}_g||$$

where $\vec{F}_g$ is the gravitational force, $m$ is the mass, $\vec{g}$ is the gravitational acceleration, $W$ is the weight. The magnitude of the gravitational acceleration $g$ is about $9.79\ m/s^2$ in Austin.

In daily language, mass is more like how few or many atoms an object has, and weight is more like how light or heavy an object is. As you can imagine, an object has the same amount of mass on Earth and on the moon, but it is lighter on the moon than on Earth. In fact, because Earth is not a perfect sphere, gravity is stronger near the poles than near the equator. Therefore, an object is heavier near the poles than near the equator, though its mass does not change.