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high school physics Newton's Laws of Motion

Newton's laws of motion are three: inertia, by which an object keeps doing what it was doing when the net force is 0; the relation F = ma between net force and acceleration; and action and reaction, by which two objects push on each other with forces equal in size and opposite in direction. Your body lurches forward when a bus brakes hard because of inertia, and a wall pushes back on you as hard as you push it because of action and reaction. The F in F = ma is the net force, the sum of all forces on the object, and the larger the mass, the harder it is to change the velocity with the same force. In the picture, a horizontal force F acts on a box on a frictionless floor; doubling the force doubles the acceleration arrow, and doubling the mass halves it.

The Three Laws of Motion

🍎 The Three Laws at a Glance
①Law 1 (law of inertia): when the net force is 0, an object at rest stays at rest and a moving object keeps moving at the same velocity
②Law 2 (law of acceleration): the larger the net force and the smaller the mass, the larger the acceleration, so F = ma
③Law 3 (action and reaction): if A pushes B, B pushes A with a force of the same size in the opposite direction

Seeing F = ma

5 kg
20 N
💡 Reading the Picture
①With the mass fixed, a larger force lengthens the acceleration arrow in the same proportion
②With the force fixed, a larger mass makes the box bigger and the acceleration arrow shorter
③The normal force N and gravity mg are equal and opposite, so the vertical net force is 0 and only the horizontal force F is left as the net force
④Mass measures how strongly an object resists a change in velocity, that is, the size of its inertia

Newton's Second Law

Newton's Second Law
F = ma
Force (N) = mass (kg) × acceleration (m/s²)
Solved for Acceleration
a = Fm
Acceleration is proportional to the net force and inversely proportional to the mass
Unit of Force: the Newton (N)
1 N = 1 kg · m/s²
1 N is the force that gives a 1 kg object an acceleration of 1 m/s²

Action and Reaction

🤝 Law 3: Forces Come in Pairs
①When your hand presses on a desk, the desk pushes your hand up with a force of the same size
②When a rocket pushes gas backward, the gas pushes the rocket forward
③Action and reaction act on different objects, so they never cancel within a single object
④N and mg in the picture are equal and opposite, but both act on the box, so they are not an action-reaction pair

Worked Examples

Example 1
A 4 kg object is acted on by a net force of 12 N. What is its acceleration?
1
From Newton's second law F = ma, a = F/m.
a = Fm
2
Substitute F = 12 N and m = 4 kg.
a = 124 = 3 m/s2
▸ 3 m/s²
With the same 12 N on an object twice as heavy, 8 kg, the acceleration would be half as large, 1.5 m/s².
Example 2
A 2 kg object is pushed with a force of 10 N, but 4 N of friction acts in the opposite direction. What is its acceleration?
1
The F in F = ma is the net force, so first subtract the friction acting the other way from the pushing force.
Fnet = 10 − 4 = 6 N
2
Compute a = Fnet/m.
a = 62 = 3 m/s2
▸ 3 m/s²
Putting in the full 10 N without subtracting friction gives 5 m/s², which is wrong.

Summary

The Core of Newton's Laws
Fnet = ma (net force = mass × acceleration)
Law 1: with zero net force, rest or uniform straight-line motion continues; Law 2: F = ma; Law 3: F₁₂ = −F₂₁
CSAT-style problem, adapted
On a frictionless floor, a 3 kg and a 2 kg object are connected by a string and pulled with 10 N. What is their acceleration?
①1 m/s²
②2 m/s²
③3 m/s²
④4 m/s²
⑤5 m/s²
▸ ② 2 m/s²
1
The two objects tied by the string move with the same acceleration, so treat them as one body and find the total mass.
mtotal = 3 + 2 = 5 kg
2
Apply F = ma to the whole system.
a = 105 = 2 m/s2
🎯 Exam Points
①The F in F = ma is the net force, the vector sum of all forces on the object
②The larger the mass, the larger the inertia and the harder it is to change the motion
③Action and reaction are a pair of forces between two objects, not two forces on one object
④For an object on a horizontal surface, N = mg only when no other vertical force acts; write F = ma for the horizontal direction
⑤Start by drawing every force on the object (a free-body diagram), then write the equations
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Uniformly Accelerated Motion
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Momentum and Impulse

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