Newton's 3 Laws · Inertia · Momentum · Work-Energy · Collisions — fully animated
Mechanics deals with motion. It has two branches:
Describes motion without discussing its cause. Parameters: distance, velocity, acceleration.
Describes motion WITH its cause — force and torque. Parameters: momentum, force, energy.
Stated that "an external force is required to keep a body in uniform motion." He was WRONG.
Objects stop because of opposing forces — friction, air resistance, viscous drag. Without these, motion continues forever!
Every object continues to be in its state of rest OR uniform unaccelerated motion unless acted upon by an external, unbalanced force.
Rate of change of linear momentum is directly proportional to applied force and in the direction of force.
To every action force, there is an equal and opposite reaction force. They act on DIFFERENT objects and NEVER cancel each other.
Inertia is the fundamental property of every object to resist change in its state of motion. Inertia is measured by mass. More mass = more inertia.
F = dp/dt — NOT F = ma. F = ma is only valid when mass is constant. For rockets, both mass AND velocity change, so we need the full form.
Gravitational force between Earth and Moon is a non-contact action-reaction pair. Magnetic repulsion between two magnets is also a non-contact pair.
Watch what happens when the car suddenly brakes. The passenger keeps moving forward — that is Newton's First Law / Inertia in action!
A frame where Newton's First Law holds. No net force → no acceleration. Body moves with constant velocity.
Accelerating frame. Objects appear to accelerate even with no real force — need to add pseudo force −ma⃗.
In a non-inertial frame of acceleration a⃗, we add a pseudo force of −ma⃗ to all objects to apply Newton's laws. It is measurable but not a fundamental force.
| Force | Strength | Range | Examples |
|---|---|---|---|
| Gravitational | Weakest | Infinite | Weight, planetary orbits |
| Electromagnetic | Strong | Infinite | Friction, normal force, tension |
| Strong Nuclear | Strongest | < 10⁻¹⁴ m | Binds nucleons in nucleus |
| Weak Nuclear | Weak | < 10⁻¹⁶ m | Radioactive beta decay |
From Newton's 2nd law: F⃗ = dp⃗/dt. If net external force = 0, then dp⃗/dt = 0, which means momentum is constant!
Work done by a force equals the change in kinetic energy of the object.
W = F⃗ · s⃗ = F·s·cosθ. For variable force: W = ∫F·ds (area under F-s graph)
Work done by net force = Change in KE = ½mv² − ½mu²
Work done is independent of path — depends only on start and end points. Gravitational force, spring force are conservative. dU = −F·dx
Friction, air drag — work done is path-dependent. Energy appears as heat/sound and is NOT recoverable.
During ALL collisions, linear momentum is conserved. But kinetic energy may or may not be conserved.
Both momentum AND kinetic energy are conserved. Coefficient of restitution e = 1.
Momentum conserved but KE is lost. Perfectly inelastic: objects stick together. e = 0.
For masses m₁ and m₂ with initial velocities u₁ and u₂ in a head-on elastic collision:
v₁ = u₂ and v₂ = u₁ — the bodies simply exchange their velocities. Ball A stops, ball B moves with A's original speed.
v₁ ≈ u₁ (heavy barely slows), v₂ ≈ 2u₁ (light moves at double the heavy body's speed).
v₁ ≈ −u₁ (light rebounds with same speed), v₂ ≈ 0 (heavy barely moves). Like a ball bouncing off a wall.
Watch elastic collision between equal masses. Ball A hits stationary Ball B — A stops completely, B moves with A's original velocity. Velocities are exchanged!
Force is NOT needed to maintain motion. Objects stop due to friction and resistance — not because motion "runs out".
No external force → no change in motion. Inertia ∝ mass. Both rest and uniform motion are "states of motion".
Force = rate of change of momentum. For constant mass: F = ma. For rockets: use full dp/dt form.
Forces come in pairs on DIFFERENT objects. They are equal and opposite. They do NOT cancel each other.
Total momentum of isolated system = constant. Used for all collision and explosion problems.
Elastic (e=1): both p and KE conserved. Perfectly Inelastic (e=0): only p conserved, objects stick. 0<e<1: partially inelastic.