PHSX 220 Physics I (w/ Calculus) · Unit 1: Kinematics & Newton’s laws · on Exam 1
Ch 5.1–5.5 Newton’s laws of motion
Study notes for Newton’s laws of motion in PHSX 220 Physics I (w/ Calculus) at Montana State University: the big ideas, key formulas, a worked example, common mistakes and an exam tip. The same topic has endless practice questions and flashcards in Mathub.
Big ideas
- First law: with zero net force an object keeps a constant velocity (including staying at rest). "At rest" and "moving at constant speed in a straight line" are the same situation dynamically.
- Second law: $\sum\vec F = m\vec a$. Net force and acceleration point the same way. Apply it separately in $x$ and $y$: $\sum F_x = ma_x$, $\sum F_y = ma_y$.
- Third law: forces come in pairs acting on different objects, equal in magnitude and opposite in direction. The pair of "Earth pulls on ball" is "ball pulls on Earth", never the normal force.
- Mass measures inertia (kg) and is the same everywhere; weight $w = mg$ is a force (N) and depends on $g$.
- Forces are interactions: every force on your object comes from something touching it (contact forces: normal, tension, friction, push) or from gravity (long range). Name the agent for each.
Key formulas
Second law
$$\sum\vec F = m\vec a\qquad \sum F_x = ma_x,\quad \sum F_y = ma_y$$
Weight
$$\vec w = m\vec g,\qquad g = 9.8\ \text{m/s}^2$$
Worked example
A 3.0 kg box on frictionless ice is pushed by 12 N eastward and 9 N northward. Find its acceleration.
Show the solution
$F_{\text{net}} = \sqrt{12^2 + 9^2} = 15$ N at $\tan^{-1}(9/12) = 36.9^\circ$ north of east. $a = 15/3 = 5.0\ \text{m/s}^2$ in that direction.
Common mistakes
- Including a "force of motion" or "force of the throw" on a ball already in flight. Only gravity (and drag) act on it.
- Pairing weight with the normal force as a third-law pair. Both act on the same object, so they cannot be a pair.
- Assuming a larger mass exerts a larger force on a smaller one in a collision. The forces are equal; the accelerations differ.
Exam tipClicker questions test the third law constantly: a truck and a bug hitting each other feel equal forces. Say it out loud until it is automatic.
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