Ch 4Laws of Motion — Class 11 Physics, concept-first.

Mechanics is the branch of physics concerned with motion. It splits naturally into two large domains: statics, the study of objects at rest or in equilibrium under balanced forces, and kinetics, the s…

Before Newton, Aristotle (384-322 BC) proposed that a body needs a continuous external force merely to keep moving at constant velocity -- his reasoning being everyday observations such as a rolling b…

Newton's three laws of motion, in their classical statement, are:

The first law is never used directly to solve a numerical problem, yet it is indispensable conceptually, contributing three distinct ideas.

The second law's real contribution is turning force into a precise, MEASURABLE, mathematical quantity: the rate of change of linear momentum, .

The third law states that action and reaction are always an equal-and-opposite PAIR of forces, acting along the same line, and -- crucially -- always acting on two DIFFERENT bodies, never on the same…

A frame of reference is simply a set of coordinates with a chosen origin used to describe the position of objects.

Having established what a force DOES (change momentum, per Newton's second law), this section turns to classifying the different KINDS of forces a body can experience, along several independent and ov…

All the forces observed in nature are ultimately manifestations of just FOUR fundamental interactions.

Forces can also be classified by whether physical contact between objects is required.

Consider standing inside a lift (elevator). When the lift starts moving UPWARD (accelerating upward), you feel heavier, as though someone is pushing you down -- and this is not imaginary: a weighing s…

A force is called CONSERVATIVE if the work done by (or against) it, in moving an object between two points, is independent of the actual path taken -- it depends only on the initial and final position…

The simple formula (with the angle between the applied force and the displacement ) is valid ONLY when both the force and the displacement are constant, finite vectors.

The WORK-ENERGY THEOREM connects the work done by a force with the resulting change in an object's kinetic energy.

From Newton's second law, ; if the resultant (net) force is zero, the linear momentum does not change -- it stays constant, i.e. it is CONSERVED.

A COLLISION is an interaction in which two or more objects come close, exert mutual forces on each other for a brief interval, and then move apart (scatter) in generally different directions/speeds th…

Collisions are classified into two broad types based on whether kinetic energy is conserved.

A PERFECTLY INELASTIC collision is the special, extreme case of an inelastic collision in which the colliding bodies join together (stick) and move off with one COMMON final velocity after impact.

For a HEAD-ON collision (where the colliding bodies move strictly along one common straight line, both before and after impact), the COEFFICIENT OF RESTITUTION e is defined as the negative of the rati…

Combining the elastic-collision relation (from e=1) with conservation of momentum, , and eliminating , gives the general formulas for the final velocities after a head-on ELASTIC collision:

For a PERFECTLY INELASTIC head-on collision of masses , with initial velocities , , the bodies move together afterwards with one common final velocity v; conservation of momentum, , immediately gives…

When at least one of the initial velocities is NOT directed along the common line joining the two colliding bodies, the collision is OBLIQUE (non-head-on, or two-dimensional).

Newton's first law says an unbalanced force changes momentum; the second law makes this precise, , so .

Impulse earns its own name and definition because, in many everyday situations, an appreciably large force acts for an extremely short interval of time -- too short to measure the force and the time i…

When opening a door, applying the force far from the hinge (and roughly perpendicular to the door) makes it easy to open; applying the same force close to the hinge, or nearly parallel to the door, ma…

In the discussion of torque above, a single force acting on a body pivoted about a fixed axis was considered -- but in that case there is necessarily a reaction force at the fixed axis itself.

This sub-section proves algebraically that the torque of a given couple does not depend on where the (fixed) axis of rotation happens to be placed.

As a direct consequence of Newton's second law, the momentum of a system stays constant whenever no external unbalanced force acts on it -- this state is called MECHANICAL EQUILIBRIUM.

A body resting under the action of balanced forces is in mechanical equilibrium, but there are three qualitatively different TYPES of such equilibrium, distinguished by what happens when the body is s…

Newton's laws of motion, as originally stated, strictly apply to POINT masses only. Real objects, however, always have a finite, measurable size and an internal distribution of mass.

For a system of n discrete particles of masses (total mass ) with position vectors from some chosen origin O, the position vector of the CENTRE OF MASS from the same origin is the mass-weighted averag…

Just as the centre of mass position is the mass-weighted average of the individual particles' positions, the VELOCITY of the centre of mass of a system of particles (with velocities ) is the mass-weig…

In exactly the same way, the ACCELERATION of the centre of mass of a system of particles (with accelerations ) is the mass-weighted average of the individual accelerations: , again with x, y, z compon…

The centre of mass has a number of important general characteristics worth collecting together: (1) it is a hypothetical point at which the entire mass of a body can be assumed concentrated; (2) it is…

The CENTRE OF GRAVITY (c.g.) of a body is the point about which the resultant torque, due to the force of gravity acting on every part of the body, is zero -- it is, in effect, the weighted average lo…