Newton's first and second laws
Force does not cause motion, it causes change in motion, and the bigger the mass, the weaker the change.
Inertia and the first law
An object with no net force on it keeps moving in a straight line at constant speed, or stays at rest. Motion at constant velocity needs no explanation; only changes in velocity do. Mass is the measure of inertia, the resistance to having your velocity changed.
\sum \vec{F} = 0 \implies \vec{v} = \text{constant}The second law
Net force equals mass times acceleration, and both force and acceleration are vectors pointing the same way. The forces must be added as vectors before multiplying by mass, and the unit is the newton: 1 N = 1 kg times m/s^2. Note the net force is what matters, not any individual force.
\vec{F}_{\text{net}} = m\vec{a}, \quad 1 \text{ N} = 1 \ \text{kg}\cdot\text{m/s}^2Worked example
A 1200 kg car accelerates from rest to 24 m/s in 8.0 s. The acceleration is (24 - 0)/8.0 = 3.0 m/s^2, so the net force is 1200 times 3.0 = 3600 N. That is the net force, not the engine force: friction and drag push backward, and the engine must supply more than 3600 N to win that tug-of-war.
F = ma = (1200)(3.0) = 3600 \text{ N}Flashcard
Net force equals mass times acceleration
Check your understanding
A 2.5 kg object is pushed by a 3.0 N force east and a 4.0 N force north at the same time. What is the magnitude of its acceleration?