Susskind Lecture 3 - Classical Mechanics
Lecture 3 moves from kinematics to dynamics. Kinematics describes motion; dynamics explains how motion changes.
The big conceptual replacement is this: force does not determine velocity. In Newtonian mechanics, force determines acceleration.
Aristotle versus Newton
An Aristotelian-style law says motion is directly tied to force: push harder, get more velocity; stop pushing, motion naturally dies away. That picture matches friction-heavy everyday intuition, but it is not the clean law of ideal mechanics.
Newton’s version is:
F = m aor in one coordinate:
F = m x_ddotA nonzero force changes velocity. If the net force is zero, velocity stays constant.
Mass as inertia
Mass measures resistance to acceleration. For the same force:
larger m ⇒ smaller aThis is why force, mass, and acceleration form one connected definition in elementary mechanics.
Force fields
A force can depend on position, time, velocity, or other particles. In the early lectures Susskind focuses on forces depending on position, because those lead naturally to potential energy in Susskind Lecture 5 - Energy.
Harmonic oscillator
The harmonic oscillator is the central example:
F = -k x
m x_ddot = -k x
x_ddot = -ω^2 x
ω = sqrt(k/m)The minus sign is the physical content: displacement produces a restoring force back toward equilibrium.
A standard solution is:
x(t) = A cos(ωt) + B sin(ωt)The constants A and B are fixed by initial position and velocity.
Why this lecture matters later
- Susskind Lecture 4 - Systems of More Than One Particle turns Newton’s second-order laws into first-order phase-space laws.
- Susskind Lecture 5 - Energy shows when forces come from a potential.
- Susskind Lecture 6 - Principle of Least Action re-derives Newton’s equation from stationary action.
- Susskind Lecture 8 - Hamiltonian Mechanics turns the oscillator into circular motion in phase space.
Common pitfalls
- Thinking a continuous push is required to maintain constant velocity. In ideal Newtonian mechanics, force changes velocity.
- Confusing the sign of the spring force. F = -kx points opposite displacement.
- Treating friction-heavy intuition as fundamental. Friction is an emergent, dissipative complication.
- Forgetting that second-order equations need two initial data: position and velocity.