Newton's Laws of Motion & Friction

Newton's Laws of Motion form the foundation of classical mechanics, connecting forces to the motion of objects. Every JEE problem in mechanics ultimately traces back to these laws.

Newton's First Law (Law of Inertia): A body remains at rest or in uniform motion in a straight line unless acted upon by a net external force. This defines inertial frames of reference — frames where the first law holds. The Earth's surface is approximately inertial for most JEE problems.

Newton's Second Law: The net force on a body equals its mass times acceleration: $F_{net}$ = ma. Dimensional formula of force: [MLT^{-2}], SI unit: Newton (N). One Newton is the force required to accelerate 1 kg by 1 m/$s^{2}$. This law applies to the CENTER OF MASS of a system.

Newton's Third Law: For every action, there is an equal and opposite reaction. Action-reaction pairs act on DIFFERENT bodies. They cannot cancel each other because they don't act on the same object.

Free Body Diagram (FBD): The most critical tool in Newtonian mechanics. Isolate the body, draw ALL forces acting ON it (weight, normal, tension, friction, applied force), and apply $F_{net}$ = ma along chosen axes.

Friction opposes relative motion (kinetic) or tendency of relative motion (static).

• Static friction: $f_{s}$ <= $\mu_{s}$ * N (self-adjusting up to maximum)
• Kinetic friction: $f_{k}$ = $\mu_{k}$ * N (constant, always less than max static)
• $\mu_{s}$ > $\mu_{k}$ always. SI units: dimensionless (no units).

Connected Systems: For bodies connected by strings/pulleys:

• Massless, inextensible string: tension is the same throughout
• Constraint relation: acceleration of connected bodies follows string length conservation

Pseudo Force: In a non-inertial frame accelerating at $a_{0}$, a pseudo force $F_{pseudo}$ = -ma_0 acts on every body (opposite to the frame's acceleration). Mass m, acceleration of frame $a_{0}$.

The key problem-solving concept is: draw the FBD for EACH body separately, apply Newton's second law along appropriate axes, and solve the resulting system of equations simultaneously.

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