Force and Laws of Motion

• What force is; balanced vs unbalanced forces.
• Newton's First Law — inertia.
• Newton's Second Law — F = ma; momentum.
• Newton's Third Law — action-reaction.
• Conservation of momentum — applications.

Force

• Force: a push or pull that can change the state of rest or motion of an object.
• Unit: Newton (N) = kg·m/s²
• Force is a vector — has both magnitude and direction.
• Balanced forces: net force = 0 → no change in motion (object stays still or keeps moving at constant velocity).
• Unbalanced forces: net force ≠ 0 → object accelerates (changes speed or direction).

Newton's First Law of Motion (Law of Inertia)

An object at rest remains at rest, and an object in motion continues in motion at the same speed and in the same direction, unless acted upon by an unbalanced external force.

• Also called the Law of Inertia.
• Inertia: the tendency of an object to resist any change in its state of rest or motion.
• Inertia depends on mass — more mass = more inertia.

Examples:

• A book on a table stays put → no unbalanced force.
• A passenger jerks backward when a bus starts suddenly → passenger's inertia resists change.
• A passenger jerks forward when brakes are applied → body continues forward due to inertia.
• Dust falls off a carpet when beaten → carpet moves, dust (inertia) stays behind.
• Athletes run before a long jump → inertia of motion helps carry them farther.

Momentum

• Momentum (p): product of mass and velocity.

p = m × v

• Unit: kg·m/s
• Momentum is a vector (same direction as velocity).
• A heavy slow truck may have the same momentum as a fast light bullet.
• Rate of change of momentum = Force applied.

Newton's Second Law of Motion

The rate of change of momentum of an object is proportional to the applied unbalanced force and takes place in the direction of the force.

F = ma (when mass is constant)

• F = net force (N), m = mass (kg), a = acceleration (m/s²)
• If F = 0 → a = 0 → constant velocity (First Law is a special case of Second Law).

Derivation:

• Initial momentum: p₁ = mv
• Final momentum: p₂ = mu
• Change in momentum: Δp = m(v − u)
• Rate of change: F = Δp/t = m(v − u)/t = ma

Worked examples:

• A 5 kg object accelerates at 3 m/s². Force = 5 × 3 = 15 N.
• A 1000 kg car goes from 0 to 20 m/s in 10 s. F = 1000 × (20/10) = 2000 N.

Newton's Third Law of Motion

For every action, there is an equal and opposite reaction. Action and reaction act on different objects simultaneously.

• Forces always come in pairs — they are equal in magnitude, opposite in direction, but on different bodies.
• They do NOT cancel each other (they act on different objects).

Examples:

Conservation of Momentum

When no external force acts on a system, the total momentum of the system remains constant.

Total momentum before = Total momentum after

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

Applications:

• Gun recoil: gun + bullet system. Before firing: total momentum = 0. After: bullet goes forward, gun recoils backward. m_bullet × v_bullet = − m_gun × v_gun.
• Rockets: expel gas (reaction mass) backward → rocket moves forward; no external force needed in space.
• Collisions: cars crashing, balls colliding — total momentum conserved.

Example calculation:

A 2 kg ball moving at 5 m/s collides with a 3 kg ball at rest. After collision, 2 kg ball moves at 1 m/s. Find velocity of 3 kg ball. Before: 2×5 + 3×0 = 10 kg·m/s After: 2×1 + 3×v₂ = 10 3v₂ = 8 → v₂ = 2.67 m/s

Summary table

• State Newton's First Law. What is inertia? How does mass affect it?
• A force of 20 N acts on a 4 kg object. Find acceleration.
• Why does a gun recoil when fired? Which law explains this?
• State the law of conservation of momentum and give one real-world example.
• A 1500 kg car brakes from 30 m/s to rest in 6 s. Find the braking force.

Open the Practice tab for graded questions on Force and Laws of Motion.