Newton’s First & Second Laws
- State Newton’s first law and recognize when an object is in equilibrium
- Apply Newton’s second law, ΣF = ma, to find net force or acceleration
- Distinguish mass (inertia) from weight (a force)
Inertia: velocity is the natural state
Newton’s first law says an object keeps doing what it is doing — staying at rest or moving in a straight line at constant velocity — unless a net force acts on it. Motion needs no cause; changing motion does. This resistance to change is inertia, and its measure is mass. When the forces on an object balance to zero net force, the object is in equilibrium: it may be sitting still or cruising at constant velocity, but its velocity is not changing.
The second law: net force causes acceleration
Newton’s second law makes the first quantitative. The net force — the vector sum of every force acting on an object — equals mass times acceleration, ΣF = ma. Acceleration points in the same direction as the net force and is proportional to it: double the net force and you double the acceleration; double the mass and you halve it. The word net is everything — a single force in a problem is rarely the whole story.
Mass is not weight
Mass (kilograms) measures how much matter an object has and how strongly it resists acceleration — it is the same on Earth, the Moon, or in deep space. Weight is the gravitational force on that mass, W = mg (newtons), and it changes with location because g changes. A 10 kg textbook has a mass of 10 kg everywhere, but it weighs 100 N on Earth (g = 10) and only about 17 N on the Moon.
Three horizontal forces act on a 4 kg cart on a frictionless floor: 20 N right, 6 N left, and 2 N left. Find the cart’s acceleration.
- 1.Choose right as positive and add the forces: ΣF = +20 − 6 − 2 = +12 N.
- 2.The net force is 12 N to the right, so the acceleration is to the right.
- 3.Apply ΣF = ma: 12 N = (4 kg) × a.
- 4.Solve: a = 12 ÷ 4 = 3 m/s².
Always find the net force first by adding forces as vectors, then divide by mass. Plugging a single force into ΣF = ma without summing the others is the most common way to get the acceleration wrong.
A 2 kg cart on a frictionless track feels a single net force of 10 N. What is its acceleration?
What is the weight of a 6 kg object near Earth’s surface? (g = 10 m/s²)
On the AP exam, "equilibrium" does not mean "at rest." An object moving at constant velocity has zero acceleration, so its net force is also zero. Constant velocity and rest are the same dynamical situation.
Answer the 2 checkpoints as you read.
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