Laws of Motion

Dynamics asks why motion changes, and the answer is force. Newton's first law states that a body continues at rest or in uniform straight-line motion unless acted on by a net external force. This property — the reluctance to change its state of motion — is inertia, and it is measured by mass: a loaded truck is harder to start or stop than a bicycle. The first law also tells us that no force is needed to keep a body moving at constant velocity; force is needed only to change velocity.

Newton's second law makes this quantitative. The net force equals the rate of change of momentum, $\vec{F} = \dfrac{d\vec{p}}{dt}$, which for constant mass reduces to the familiar $\vec{F} = m\vec{a}$. Force and acceleration are vectors pointing in the same direction, and the SI unit of force, the newton, is defined as the force that gives a $1\ \text{kg}$ mass an acceleration of $1\ \text{m/s}^{2}$. The second law contains the first as the special case $F = 0 \Rightarrow a = 0$.

Newton's third law says that to every action there is an equal and opposite reaction. The two forces are equal in magnitude, opposite in direction, and act on different bodies — this last point is crucial. Because action and reaction act on different objects, they never cancel each other; a book on a table pushes down on the table while the table pushes up on the book, and the book's weight is balanced by the table's push (the normal force), not by the reaction to its own weight.

For NEET, most problems reduce to drawing a free-body diagram: isolate one body, mark every force acting on it (weight, normal reaction, tension, friction, applied force), and apply $\vec{F}_{\text{net}} = m\vec{a}$ along chosen axes. Connected systems — blocks joined by strings over pulleys, or stacked blocks — are handled by writing the second law for each body and using the shared acceleration and the equal-and-opposite tensions.

Linear momentum $\vec{p} = m\vec{v}$ is the 'quantity of motion' of a body — a vector in the direction of velocity, with SI unit $\text{kg}\cdot\text{m/s}$. A heavy slow truck and a light fast bullet can carry the same momentum. Newton's second law is most fundamentally a statement about momentum: force is the rate of change of momentum, so a force changes a body's momentum over time.

Impulse measures the total effect of a force acting for a time interval: $\vec{J} = \vec{F}\,\Delta t = \Delta \vec{p}$, the impulse-momentum theorem. This explains everyday safety design — air bags, crumple zones and cushioned landings all increase the time of impact, which for the same change in momentum reduces the peak force. A cricketer drawing the hands back while catching does exactly the same thing.

The most powerful result is the law of conservation of momentum: if no net external force acts on a system, its total momentum stays constant. This follows directly from the third law — internal action-reaction forces are equal and opposite, so they cancel in pairs. The law holds even when energy is lost, which makes it ideal for collisions and explosions where forces are large and brief.

NEET applies this to three standard situations. In a recoil (a gun firing a bullet, or a person jumping off a boat), the total momentum stays zero, so the heavy body recoils slowly while the light body shoots off fast. In collisions, total momentum is always conserved; in a perfectly elastic collision kinetic energy is also conserved, while in a perfectly inelastic collision the bodies stick together and move with a common velocity. Writing 'total momentum before = total momentum after' solves the great majority of these problems.

Friction is the force that opposes relative motion (or the tendency of relative motion) between surfaces in contact. It arises from microscopic roughness and adhesion between surfaces and always acts along the surface, opposing the direction in which the body tends to slide. Though often a nuisance, friction is essential — without it we could not walk, vehicles could not grip the road, and knots would not hold.

Friction comes in stages. Static friction acts when there is no sliding yet; it is self-adjusting, growing to match the applied force up to a maximum value $f_{s,\max} = \mu_s N$, where $N$ is the normal reaction and $\mu_s$ is the coefficient of static friction. Once the applied force exceeds this limit the body starts to slide and kinetic (sliding) friction takes over, with magnitude $f_k = \mu_k N$. Experiment shows $\mu_k < \mu_s$, which is why it takes a bigger push to start a heavy box moving than to keep it moving.

A key NEET fact is what friction does not depend on. The friction force is independent of the apparent area of contact and (for kinetic friction) of the relative speed; it depends only on the nature of the surfaces (through $\mu$) and the normal force $N$. On a horizontal surface $N = mg$, but on an incline or when an external force has a vertical component, $N$ changes — and so does the friction. Mishandling $N$ is the most common source of error here.

On an inclined plane at angle $\theta$, the component of gravity along the slope is $mg\sin\theta$ and the normal reaction is $N = mg\cos\theta$. A block placed on a gradually steepened incline begins to slide at the angle of repose $\theta$, where $\tan\theta = \mu_s$ — at this angle the gravitational pull along the slope just overcomes the maximum static friction. This neat result connects the coefficient of friction to a directly measurable angle, and appears regularly in NEET.

A body moving in a circle at constant speed is in uniform circular motion. Even though the speed is unchanged, the direction of velocity changes continuously, so the body is accelerating. This acceleration points toward the centre and is called centripetal acceleration, $a_c = \dfrac{v^{2}}{r} = \omega^{2} r$, where $v$ is the speed, $r$ the radius and $\omega$ the angular velocity.

By Newton's second law, a centre-directed acceleration requires a centre-directed net force, the centripetal force $F_c = \dfrac{mv^{2}}{r} = m\omega^{2} r$. It is important to understand that centripetal force is not a new kind of force — it is the name for whatever real force provides the inward pull in a given situation: gravity for a satellite, tension for a stone whirled on a string, friction for a car on a flat road, and the normal force component for a banked road.

The so-called centrifugal force is not a real force at all; it is a pseudo-force that appears only in a rotating (non-inertial) frame, equal and opposite to the centripetal force. NEET often tests whether you can tell the genuine inward (centripetal) force from this apparent outward one. In an inertial frame, only the inward force exists.

Two applications dominate NEET. For a car on a level road, friction supplies the centripetal force, so the maximum safe speed is $v_{\max} = \sqrt{\mu r g}$ — beyond this the car skids outward. For a banked road tilted at angle $\theta$, even without friction the horizontal component of the normal force can supply the turning force, giving the design speed $v = \sqrt{rg\tan\theta}$. The vertical circle (a bucket of water swung overhead, or a loop-the-loop) is another favourite: at the topmost point, gravity and tension both point down, and the minimum speed to maintain contact is $v_{\text{top}} = \sqrt{gr}$.