Newton's Laws, Force & Friction

Newton's First Law: Inertia

Newton's First Law states that an object at rest stays at rest, and an object in motion stays in motion at constant velocity, unless acted on by a net external force. This tendency to resist a change in motion is called inertia, and an object's mass is the quantitative measure of its inertia — the more mass an object has, the more it resists acceleration.

Newton's First Law is really a special case of the Second Law: when the net force on an object is zero, its acceleration is also zero, so its velocity cannot change. An object can have many forces acting on it and still obey the First Law, as long as those forces cancel completely.

Biological context: Inertia explains why a sudden car stop causes whiplash. The torso is restrained by a seatbelt and decelerates with the car, but the head, only loosely connected by neck muscles, tends to keep moving forward at the original velocity until the neck forcibly decelerates it. Without a seatbelt, internal organs can likewise continue moving forward relative to a suddenly decelerating ribcage — a mechanism behind certain traumatic injuries discussed in MCAT passages. The same idea appears when a standing passenger lurches forward as a bus brakes: the feet slow with the floor via friction, but the upper body continues at the prior velocity until muscle forces restore upright posture.

Newton's Second Law: F = ma

Newton's Second Law relates the net force acting on an object to its mass and acceleration:

Fnet = ma

Force is measured in newtons (N), where 1 N = 1 kg·m/s². Because acceleration is a vector, so is net force — the direction of the acceleration matches the direction of the net force, not necessarily the direction of any single individual force acting on the object.

Worked example: A 70 kg patient is pushed across a frictionless hospital floor, producing an acceleration of 2 m/s². What net force is being applied?

Fnet = ma = (70 kg)(2 m/s²) = 140 N

Worked example (weight): An object's weight is the gravitational force acting on it, W = mg. A 60 kg person at Earth's surface (g ≈ 10 m/s²) has a weight of:

W = (60 kg)(10 m/s²) = 600 N

Mass and weight are frequently confused on the MCAT: mass (kg) is an intrinsic, location-independent property, while weight (N) is a force that depends on the local gravitational field and changes on the Moon or in orbit — even though the object's mass does not. A 60 kg astronaut still has mass 60 kg in orbit, but can feel "weightless" when the effective normal force is near zero during free fall around Earth.

When multiple forces act, always find net force before applying F = ma. A 100 N horizontal push against 40 N of kinetic friction produces Fnet = 60 N, not 100 N — only the unbalanced portion accelerates the object.

Newton's Third Law: Action-Reaction Pairs

Newton's Third Law states that for every force one object exerts on a second object, the second object exerts an equal-magnitude, oppositely-directed force back on the first object. These are called action-reaction pairs.

The most important exam trap: action-reaction pairs act on two different objects, so they never cancel each other out and never prevent motion. When you walk, your foot pushes backward against the ground (action); the ground pushes forward on your foot with equal magnitude (reaction). You accelerate forward because the reaction force acts on you, not because the two forces canceled — they cannot cancel, since one acts on the ground and the other acts on your foot.

This same distinction applies to a swimmer pushing water backward to move forward, and to a bird's wings pushing air downward to generate lift. In each case, the propulsive force the organism experiences is the reaction to a force it exerts on its surroundings. In the cardiovascular system, blood pushes outward on a vessel wall and the wall pushes inward on the blood with equal magnitude — those forces act on different objects (wall vs. blood), so they do not "cancel the blood's pressure" in the sense of erasing either force; each object still feels its own force.

Static and Kinetic Friction

Friction is the force that resists relative sliding between two surfaces in contact, and it comes in two forms:

• Static friction (fs) resists the start of motion between surfaces that are not yet sliding. It is a variable, self-adjusting force that matches whatever force is applied, up to a maximum: fs ≤ μsN, where μs is the coefficient of static friction and N is the normal force.
• Kinetic friction (fk) acts once surfaces are sliding, and is essentially constant: fk = μkN, where μk is the coefficient of kinetic friction.

For nearly all real surfaces, μs > μk — it takes more force to start an object sliding than to keep it sliding, which is why a stuck object suddenly gives way and accelerates once it breaks free.

Worked example: A 10 kg crate sits on a floor with μs = 0.4 and μk = 0.3. Using g ≈ 10 m/s², the normal force equals the crate's weight: N = mg = (10 kg)(10 m/s²) = 100 N.

• Maximum static friction: fs(max) = μsN = (0.4)(100 N) = 40 N
• Kinetic friction once sliding: fk = μkN = (0.3)(100 N) = 30 N

You must push with more than 40 N to get the crate moving, but once it is sliding, only 30 N is needed to keep it moving at constant velocity. If you keep pushing with the original 40+ N, the crate will now accelerate, since the opposing friction force just dropped to 30 N.

Biological and clinical notes: Friction between shoes and floor enables the backward push that produces forward walking thrust (Third Law). Too little friction (icy floor) reduces the maximum static friction available, so the foot slips before generating useful propulsion. Joint surfaces are lubricated by synovial fluid to lower μk and protect cartilage; passages may contrast dry versus lubricated contact when discussing osteoarthritis or implant materials. On a horizontal surface N = mg, but on an incline N = mg cos θ, so friction scales with the normal force, not always with the full weight.

Center of Mass

The center of mass is the single point at which an object's (or a system's) total mass can be treated as concentrated for the purposes of analyzing translational motion. For a system of two point masses along a line, the center of mass position is:

xcm = (m₁x₁ + m₂x₂) / (m₁ + m₂)

Worked example: A 4 kg mass sits at x = 0 m, and a 2 kg mass sits at x = 6 m. The center of mass is:

xcm = [(4 kg)(0 m) + (2 kg)(6 m)] / (4 kg + 2 kg) = 12 / 6 = 2 m

Notice the center of mass sits closer to the heavier mass, at 2 m rather than the geometric midpoint of 3 m — center of mass is a mass-weighted average position, not a simple geometric average.

Biological context: The human body's center of mass shifts constantly with posture and load. It rises when the arms are raised overhead, and it shifts forward and upward during pregnancy as the fetus and uterus add mass anteriorly — which is part of why balance and gait change during pregnancy, and why athletes crouch to lower their center of mass for greater stability. For a person standing quietly, the vertical line through the center of mass must fall within the base of support (the feet); if it does not, a net torque tips the body and fall-prevention muscles must fire. That rotational idea is developed fully in the next section on equilibrium and torque.

Quick force checklist for F = ma problems:

1. Identify the object of interest and draw a free-body diagram
2. Resolve angled forces into components
3. Sum forces on each axis to get Fnet,x and Fnet,y
4. Apply Fnet = ma on each axis separately
5. Never cancel Third-Law pairs that act on different objects