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Physics Unit 2: Forces and Newton's laws

Forces change motion. Newton's laws connect the net force on an object to its acceleration.

Covers: Newton's three laws, free-body diagrams, weight, normal force, friction, inclines, gravitation

Study guide

Newton's laws connect forces to motion. The first law (inertia) says an object stays at rest or keeps moving at constant velocity unless a net force acts on it. The second law says the net force causes acceleration: F_net = ma, so more force means more acceleration and more mass means less. The third law says forces come in pairs: if A pushes on B, B pushes back on A with an equal and opposite force. The pair acts on different objects, so they don't cancel.

A free-body diagram shows every force on one object as an arrow. Add the forces as vectors, usually by splitting them into x and y components, to find the net force, then apply F_net = ma in each direction. If the object is at rest or moving at constant velocity, the net force is zero (equilibrium).

Common forces: weight W = mg points down, where g = 9.8 m/s². The normal force is the perpendicular push of a surface; on a flat surface with no other vertical forces it equals mg, but it changes on inclines and in elevators. Tension pulls along ropes. Friction opposes sliding: static friction can hold up to μₛN, and kinetic friction during sliding is f = μₖN.

On an incline of angle θ, split the weight into a component along the slope, mg sin θ, and one into the surface, mg cos θ, which the normal force balances.

Newton's law of universal gravitation says every two masses attract with F = Gm₁m₂/r². Gravity follows an inverse-square law: doubling the distance cuts the force to one fourth.

A scale measures the normal force, not your weight. In an elevator accelerating upward, N = m(g + a), so you feel heavier. Accelerating downward, N = m(g − a). In free fall N = 0, and you feel weightless. When objects are connected by a string and move together, treat them as one system to find the acceleration: a = (net external force) ÷ (total mass). Then draw a free-body diagram for one object alone to find the tension. Forces between objects in the system are internal and cancel.

On an incline with kinetic friction, the net force along the slope is mg sin θ − μₖmg cos θ, so a = g(sin θ − μₖ cos θ). If μₛ ≥ tan θ, static friction holds the object at rest.

Key ideas

• First law: with no net force, velocity stays constant.
• Second law: F_net = ma.
• Third law: forces come in equal and opposite pairs acting on different objects.
• Weight W = mg; the normal force pushes perpendicular to a surface.
• Kinetic friction f = μN opposes sliding.

Formulas and rules

Common mistakes

• Putting both third-law forces on the same free-body diagram.
• Assuming the normal force always equals mg (not on inclines or in elevators).

Words to know

Newton's second law

F_net = ma.

Weight formula

W = mg.

Newton's third law

Forces come in equal, opposite pairs acting on different objects.

Kinetic friction

f = μN, opposite the motion.

Equilibrium (forces)

Net force is zero, so velocity is constant.

Newton's first law

An object keeps its velocity unless a net force acts (inertia).

Inertia

Resistance to changes in motion; depends on mass.

Free-body diagram

A sketch of every force on one object.

Normal force

A surface's perpendicular push.

Tension

The pulling force in a rope or string.

Static friction

Friction that prevents sliding, up to μₛN.

Incline components

Along the slope mg sin θ; into the surface mg cos θ.

Universal gravitation

F = Gm₁m₂/r²

Newton's three laws

Inertia; F_net = ma; equal and opposite force pairs.

Sample practice questions

21 more questions like these, from level 1 to 5, are in the practice set.