Mechanics
Kinematics, Newton's laws, work–energy, momentum, collisions, circular motion, SHM, and rigid body rotation.
Top video lessons
Introduction to Mechanics
Khan Academy
Newton's Laws of Motion
Professor Dave Explains
Work, Energy, and Power
Michel van Biezen
Momentum and Collisions
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Circular Motion
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Simple Harmonic Motion
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Interactive simulations
Notes
Kinematics
- Position, velocity, and acceleration are related by derivatives: v = dx/dt, a = dv/dt.
- For constant acceleration: v = u + at, s = ut + ½at², v² = u² + 2as.
- Projectile motion separates into independent x (uniform) and y (accelerated) components.
v = u + at
s = ut + ½at²
R = v₀² sin(2θ) / g
Newton's Laws & Forces
- 1st law: inertia — net force zero ⇒ constant velocity.
- 2nd law: ΣF = ma (vector form).
- 3rd law: action–reaction pairs act on different bodies.
- Friction: f ≤ μN (static), f = μₖN (kinetic).
ΣF = ma
f_s ≤ μ_s N
f_k = μ_k N
Work, Energy, Momentum
- Work by a constant force: W = F·s = Fs cosθ.
- Kinetic energy KE = ½mv²; work–energy theorem: W_net = ΔKE.
- Conservative forces → potential energy; mechanical energy conserved if only conservative forces do work.
- Momentum p = mv is conserved in isolated systems; collisions may be elastic or inelastic.
W = F s cosθ
KE = ½mv²
p = mv
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
Circular Motion & SHM
- Centripetal acceleration a_c = v²/r = ω²r toward center.
- SHM: restoring force F = −kx; ω = √(k/m); T = 2π√(m/k).
- Pendulum (small angle): T = 2π√(L/g).
a_c = v²/r
T = 2π√(m/k)
T = 2π√(L/g)
Full topic quiz — 100 MCQs
50 theory + 50 numerical · instant feedback on each answer
Quick practice (sample):
Quick quiz
1. A projectile is launched with speed v at angle θ. Max range on flat ground occurs at:
2. In an isolated system, which quantity is always conserved in collisions?
3. Period of a mass-spring SHM system is:
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