Laws of Motion and Momentum

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Newton's Three Laws: 1st: An object at rest stays at rest, in motion stays in motion, unless acted upon by external force. (Inertia)
2nd: F = ma. Force equals rate of change of momentum.
3rd: For every action there is an equal and opposite reaction.

Newton's three laws are the foundation of mechanics. NDA tests each law's statement, examples, and applications. Concepts of inertia, momentum, impulse, friction.

First Law — Inertia

"An object continues in its state of rest or uniform motion in a straight line unless acted upon by an unbalanced external force."

Defines the concept of force.
States the principle of inertia.
Mass is the measure of inertia. More mass = more inertia.
Galileo's contribution: Concept of inertia established earlier; Newton refined.

Second Law — F = ma

"The rate of change of momentum is directly proportional to the applied force, in the direction of the force."

F = ma (when mass is constant).
F = dp/dt (more general; p = momentum = mv).
SI unit of force: newton (N) = kg·m/s².
1 N = force needed to give a 1 kg mass an acceleration of 1 m/s².

Third Law — Action-Reaction

"For every action there is an equal and opposite reaction."

Forces always occur in pairs — never alone.
Action and reaction act on different bodies (never cancel each other).
Examples: walking (foot pushes ground back, ground pushes foot forward); rocket propulsion; recoil of gun.

Momentum and Impulse

Momentum (p) = mass × velocity. Vector quantity. SI unit: kg·m/s.
Impulse (J) = force × time = change in momentum. SI unit: N·s.
Conservation of momentum: Total momentum of isolated system is constant. m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂. Applies to collisions, recoil, explosions.

Friction

Opposes relative motion between surfaces in contact.
Static friction: When surfaces are not yet moving. Up to limiting value f_s ≤ μ_s N.
Kinetic friction: When surfaces are moving. f_k = μ_k N. Less than static.
Coefficient of friction μ depends on materials in contact.
Rolling friction << sliding friction — why we use wheels.
Friction is essential for walking, driving, gripping — and also wastes energy as heat.

NDA PYQ Examples

Q: Newton's first law defines:

(a) Force (b) Mass (c) Acceleration (d) Energy

Answer: (a) Force — as something that changes state of rest/motion.

Q: A rocket moves forward by:

(a) Newton's first law (b) Newton's second law (c) Newton's third law (d) Conservation of energy

Answer: (c) Newton's third law (and conservation of momentum) — gas ejection backward propels rocket forward.

Q: When you walk, you push backward on the ground; the ground pushes you forward. This is:

(a) Newton's 1st law (b) Newton's 2nd law (c) Newton's 3rd law (d) Inertia

Answer: (c) Newton's 3rd law.

Q: The SI unit of impulse is:

(a) Newton (b) Joule (c) N·s (d) kg·m/s²

Answer: (c) N·s (same as kg·m/s — units of momentum).

Drill Laws of Motion and Momentum for NDA

NDA-pattern items on Laws of Motion and Momentum with answer keys and explanations.

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Frequently Asked Questions

What is inertia?

The tendency of an object to remain in its current state of motion (rest or constant velocity). Mass measures inertia — more mass means more inertia, more force needed to change motion.

Why do passengers lurch forward when a bus suddenly brakes?

Inertia of motion. While the bus decelerates due to brakes, passengers' bodies continue forward because no force is decelerating them. They lurch forward until the seat belt or front of vehicle stops them.

What is the difference between mass and weight?

Mass is the amount of matter (scalar, in kg). Constant everywhere. Weight is the gravitational force on mass (vector, in N) = mg. Varies with location (less on Moon, more at sea level than mountain top).

Why is friction sometimes called a necessary evil?

Necessary — we couldn't walk, drive, hold objects, or write without it. Evil — it wastes energy as heat, wears out moving parts, and reduces efficiency of machines.

How does a seat belt save lives?

It increases the time over which a passenger decelerates. Same change in momentum spread over longer time = lower force on the body (since F = Δp/Δt). Less force = less injury.