Newtonian Mechanics
Year 1 · 5 sections · 46 concepts · 135 practice questions
What's covered
free1 · Kinematics7 concepts
- Overview 1 · The plan of this section
- Definition 1.1 · Position, velocity and acceleration
- Proposition 1.2 · Constant acceleration
- Example 1.3 · Projectile motion
- Proposition 1.4 · Hitting a target
- Proposition 1.5 · Velocity and acceleration in polar coordinates
- Check 1.6 · Check: kinematics problems
2 · Newton's laws8 concepts
- Overview 2 · The plan of this section
- Definition 2.1 · Newton's laws of motion
- Definition 2.2 · Weight, normal reaction and tension
- Definition 2.3 · Friction
- Proposition 2.4 · Equilibrium of a particle
- Example 2.5 · Connected particles (Atwood machine)
- Proposition 2.6 · Linear resistance and terminal velocity
- Check 2.7 · Check: force diagrams
3 · Energy and momentum11 concepts
- Overview 3 · The plan of this section
- Definition 3.1 · Work and kinetic energy
- Theorem 3.2 · Work–energy theorem
- Definition 3.3 · Conservative forces and potential energy
- Theorem 3.4 · Conservation of energy
- Definition 3.5 · Power
- Definition 3.6 · Momentum and impulse
- Theorem 3.7 · Conservation of momentum
- Definition 3.8 · Newton's law of restitution
- Proposition 3.9 · Direct collision of two spheres
- Check 3.10 · Check: energy or momentum?
4 · Oscillations9 concepts
- Overview 4 · The plan of this section
- Definition 4.1 · Simple harmonic motion
- Proposition 4.2 · Speed and energy in SHM
- Example 4.3 · Mass on a spring
- Proposition 4.4 · The simple pendulum
- Theorem 4.5 · Small oscillations about a stable equilibrium
- Proposition 4.6 · Damped oscillations
- Proposition 4.7 · Forced oscillations and resonance
- Check 4.8 · Check: oscillation problems
5 · Central forces and orbits11 concepts
- Overview 5 · The plan of this section
- Proposition 5.1 · Circular motion
- Example 5.2 · Conical pendulum, banked tracks and vertical circles
- Definition 5.3 · Angular momentum and torque
- Proposition 5.4 · Rate of change of angular momentum
- Theorem 5.5 · Central forces conserve angular momentum
- Corollary 5.6 · Equal areas in equal times
- Proposition 5.7 · Radial equation and effective potential
- Proposition 5.8 · Circular orbits and Kepler's third law
- Theorem 5.9 · Kepler's laws
- Check 5.10 · Check: orbit problems
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Proposition 1.2 · Constant acceleration
Constant acceleration: , , . Only valid for constant .
Proof
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