5.1 Mass, Force, Inertia & Newton's Laws

Mass, Force, Inertia & Newton's Laws

Dynamics studies the relationship between force and motion. Where statics dealt with balanced loads (ΣF = 0, ΣM = 0), dynamics deals with unbalanced forces that produce acceleration. Module 2 expects precise use of mass, weight, inertia, and Newton’s three laws, all in SI units, with aviation examples such as thrust, braking, and towing.

Mass Versus Weight — The Core Exam Trap

Mass is the quantity of matter in a body. It is a scalar property, independent of location (same mass on Earth, in cruise, or on the Moon). The SI unit is the kilogram (kg). Mass also measures how strongly a body resists changes in motion — that resistance is inertia.

Weight is the gravitational force attracting the body toward the Earth (or other planet). Weight is a force, so its SI unit is the newton (N). Near Earth’s surface:

W = m g

where g ≈ 9.81 m/s² (often 9.81 or 10 m/s² in exam approximations). A mass of 100 kg has weight:

W = 100 × 9.81 = 981 N (about 1 000 N if g = 10 m/s²)

In everyday speech people say “this weighs 100 kg,” but that language is dimensionally wrong for physics. On the Module 2 paper:

• If the question asks for mass, answer in kg.
• If it asks for force, load, or weight in SI, answer in N.
• Never write F = m without converting weight when the given “load” is in kg and you need newtons for F = ma.

Worked example — conversion. An engine module has mass 250 kg. Its weight on Earth is W = 250 × 9.81 = 2 452.5 N ≈ 2.45 kN. A hoist must support at least this force (plus dynamic factors if the load is jerked).

Weight changes with g; mass does not. At high altitude g is slightly smaller, and in free fall or orbital flight the body is weightless relative to the cabin while its mass and inertia remain fully present — a tool still needs force to accelerate it.

Inertia

Inertia is the property of matter that resists any change in its state of rest or of uniform motion in a straight line. A heavy trolley on a hangar floor is hard to start moving and hard to stop once rolling — large mass means large inertia. A light composite panel is easy to accelerate and easy to stop.

Key points:

• Inertia is not a force; it is a property quantified by mass.
• No external force is “needed to keep something moving” in the ideal frictionless case — that misconception confuses inertia with the need to overcome drag or friction.
• Seat belts and cargo restraints exist because passengers and freight have inertia: when the aircraft decelerates, the mass tends to continue forward at the previous velocity until a force (belt load, net) changes its momentum.

Newton’s First Law (Law of Inertia)

A body remains at rest, or continues to move in a straight line at constant speed, unless acted upon by a net external force.

If ΣF = 0, acceleration a = 0. Rest and constant-velocity straight-line motion are the same dynamical state: zero net force. An aircraft in steady, level, unaccelerated flight has lift balancing weight and thrust balancing drag — net force (and net moment for equilibrium) zero, even though large individual forces act.

Applications:

• Tools left unsecured on a work stand stay put only until the stand is jolted; then they slide (net force from friction may be insufficient).
• An aircraft on a frictionless ideal surface would not stop after thrust is cut — real aircraft stop because of drag, rolling resistance, and brakes.
• Turning flight requires a net horizontal force (centripetal force from banked lift); without it the aircraft would continue straight (first-law behaviour).

Newton’s Second Law (F = ma)

The acceleration of a body is proportional to the net force acting on it and inversely proportional to its mass, in the direction of the net force.

In SI units the constant of proportionality is 1, so:

ΣF = m a

or, for a single resultant force along a line, F = m a.

• F is net force in newtons (N)
• m is mass in kilograms (kg)
• a is acceleration in metres per second squared (m/s²)

Definition of the newton: 1 N = 1 kg·m/s² — the force that accelerates 1 kg at 1 m/s².

Worked example — linear acceleration. A baggage cart has mass 400 kg. A tow tractor applies a horizontal force of 600 N; rolling resistance is 100 N opposite to motion. Net force F_net = 600 − 100 = 500 N.

a = F_net / m = 500 / 400 = 1.25 m/s²

If the same net force acted on a 800 kg cart, a would be only 0.625 m/s² — double the mass, half the acceleration.

Worked example — thrust and take-off. An aircraft mass 20 000 kg experiences average net accelerating force (thrust − drag − rolling resistance) of 40 000 N during the early ground roll.

a = 40 000 / 20 000 = 2.0 m/s²

From rest, speed after 20 s of constant acceleration: v = a t = 2.0 × 20 = 40 m/s (using kinematics from Chapter 4). Dynamics supplies a; kinetics converts a into speed and distance.

Weight as a force in free fall. In free fall with no air resistance, the only force is weight: F = mg, so a = F/m = g. All masses fall with the same acceleration g if drag is negligible — mass cancels. With drag present, terminal velocity depends on shape and mass because drag force grows until it balances weight.

Vector Nature of the Second Law

Force and acceleration are vectors. You must resolve forces into components, find ΣF_x and ΣF_y, then a_x = ΣF_x / m and a_y = ΣF_y / m. A parked aircraft on a level ramp has ΣF_horizontal = 0 if chocks and brakes hold it; on a sloping ramp a component of weight m g sin θ down the slope must be balanced by brakes or chocks, or the aircraft accelerates downhill.

Worked example — slope. Mass 5 000 kg on a 5° ramp (ignore rolling resistance). Component down the slope: F = m g sin 5° ≈ 5 000 × 9.81 × 0.0872 ≈ 4 280 N. If unrestrained, a = F/m ≈ 0.856 m/s² down the slope.

Newton’s Third Law (Action and Reaction)

Whenever body A exerts a force on body B, body B exerts a force equal in magnitude, opposite in direction, and collinear on body A.

Action and reaction act on different bodies. They never cancel each other on a single free-body diagram of one body only — that is a common exam trap. On the free body of the aircraft you draw thrust from the engine/propulsion system and drag from the air; you do not cancel thrust with “the reaction on the exhaust gas” on the same diagram, because that reaction force acts on the gas, not on the airframe alone in the simplified model. Propulsion works because the engine pushes fluid backward and the fluid pushes the engine (and aircraft) forward.

Aviation and hangar examples:

• Jet/propulsion: engine accelerates mass of air/gas aft; equal forward force on the engine mount structure.
• Helicopter: rotor pushes air down; air pushes rotor (and aircraft) up — lift.
• Landing gear: tyre pushes down and aft on the runway during braking; runway pushes up (normal reaction) and forward (friction) on the tyre.
• Towing: tractor pulls towbar; towbar pulls tractor aft with equal force — the tractor must have enough drive traction to accelerate both itself and the aircraft.

Worked example — third-law pair. A mechanic pushes a workstand with 150 N horizontal force. The workstand pushes back on the mechanic with 150 N. If the stand’s mass is 50 kg and floor friction on the stand is 30 N, net force on the stand is 150 − 30 = 120 N, so a_stand = 120/50 = 2.4 m/s². The force on the mechanic is a separate free-body problem (friction under the mechanic’s feet must exceed 150 N or the mechanic slips).

Linking the Three Laws

The first law is the special case of the second when ΣF = 0. The third law is about interaction pairs, not about the net force on one body.

Practical Maintenance Links

• Weighing and mass & balance use mass (or weight converted carefully); structural loads and jack capacities are forces in N or kN.
• Engine run-up: thrust (force) on the airframe must be reacted by brakes and tiedowns — third law and free-body thinking.
• Cargo restraint: during take-off acceleration and landing deceleration, unrestrained mass continues at previous velocity relative to inertial space until a restraint force accelerates it with the aircraft (first and second laws).
• G-loading: a 2 g pull-up means the structure and seats must supply force ≈ 2 mg on the mass; apparent weight doubles.

Formula and Unit Checklist

• m in kg; W = m g in N; g ≈ 9.81 m/s²
• ΣF = m a; 1 N = 1 kg·m/s²
• Mass ≠ weight; inertia quantified by mass
• Action–reaction on different bodies
• Always use net force in F = m a

Master mass versus weight and the three laws with SI units and you have the foundation for work, energy, momentum, and every later force–motion topic in Module 2.