Lec 06: Newton's First, Second, and Third Laws | 8.01 Classical Mechanics, Fall 1999 (Walter Lewin)

Scientific concepts, discoveries, and nature phenomena

Newton’s Laws of Motion (origin and statements)

• First Law / Law of Inertia

  • Concept: A body maintains rest or constant velocity in a straight line unless acted upon by a net external force.
  • Historical sources mentioned:
    • Galileo’s “law of inertia” (paraphrased and quoted).
    • Isaac Newton’s statement in Principia (quoted).

• Inertial reference frames

  • Newton’s laws require an inertial frame (one that is not accelerating).
  • A lecture hall (Earth-based) is treated as approximately inertial because Earth’s centripetal accelerations are small compared with gravity.

  • Earth’s accelerations discussed:

    • Due to Earth’s rotation: [ a_c=\omega^2 R ] estimated as ~0.034 m/s² at the equator.

    • Due to Earth’s orbit around the Sun: even smaller by an additional factor (about 5× lower).

• Second Law (definition of force; (F=ma))

  • Experimental/operational idea with a spring:

    • Apply the same “pull” (spring extension) to different masses and measure resulting accelerations.

    • Empirical finding: [ m_1 a_1 = m_2 a_2 ] for the same pull.

    • Force is defined operationally as: [ F \equiv ma ]

  • Newton’s statement: Force produces acceleration in the direction of the force, with magnitude (F=ma).

  • Range of validity:
    • Newtonian mechanics applies for speeds well below the speed of light.
    • At speeds approaching (c), use Einstein’s special relativity.

• Third Law (action–reaction)

  • Statement: If one object exerts a force on another, the second exerts an equal-magnitude opposite-direction force on the first.
  • Notation emphasized: “Action equals minus reaction.”
  • Key point: Holds regardless of motion/acceleration; forces occur as pairs.

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Nature/physical demonstrations and worked examples

Everyday manifestations of action–reaction

• Walking: pushing against the floor; the floor pushes back.
• Gun recoil: bullet and gun exert equal and opposite forces.
• Rocket idea (air/balloon example): expelled air pushed backward; balloon/rocket pushes forward.
• Swimming / “priestess story” + Hero’s engine
  • A steam/water-jet device rotates because exiting fluid provides thrust via action–reaction.
  • “Hero’s engine” described historically (Greek legend).

Weird but instructive consequence: mutual attraction of Earth and falling objects

• Example: an apple falls ~100 m under gravity.

• Using [ h=\tfrac{1}{2}gt^2 ] the estimated time is ~4.5 s.

• By Newton’s Third Law, Earth experiences the equal opposite force to the apple’s gravitational force:

  • apple feels approximately (mg \approx 5) N (using (g \approx 10) and (m \approx 0.5) kg)
  • Earth’s acceleration becomes extremely tiny: [ a_E=\frac{F}{M_E}\sim 8\times 10^{-25}\ \text{m/s}^2 ]

• Earth displacement over ~4.5 s is correspondingly minuscule (~(8\times 10^{-24}) m), but conceptually Earth “falls toward” the apple.

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Statics / equilibrium with tensions in strings

Setup (two-string equilibrium)

• A mass (m) hangs from two strings attached to a ceiling:
  • One string makes 60° with the vertical (equivalently 30° with the horizontal).
  • The other string makes 45° with the vertical.
• Assumptions:
  • Strings are massless.
  • System is not accelerating ⇒ net force = 0.

Method: coordinate decomposition

• Choose axes (x) and (y), requiring:
  • (\sum F_x = 0)
  • (\sum F_y = 0)

• Use trigonometric components:

  • [ T_1\cos 60^\circ - T_2\cos 45^\circ = 0 ]

  • [ T_1\sin 60^\circ + T_2\sin 45^\circ - mg = 0 ]

• Solve for tensions (T_1) and (T_2).

Results for an example

For (m=4) kg with (g\approx 10):

• (T_1 \approx 29.3) N
• (T_2 \approx 20.7) N

Alternative method mentioned

• Treat the three forces as a triangle (vector addition) using the known angles, without explicit (x/y) decomposition.

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Measurement of tension

• Tension meters described conceptually:
  • Use spring scales to infer tension from extension (force balance under no acceleration).
• Practical note: angle alignment errors and scale uncertainty can affect measured values.

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Counterintuitive “which string breaks” tension-sharing demonstration

• A mass (~2 kg block) is supported by two nearly identical strings:
  • Upper string tension is near (T_1 \approx 20) N (to support the block’s weight).
  • Lower string tension is near 0 (as described in the initial setup).
• Procedure/method:
  • Slowly increase applied tension on one side (the lower one) until one string breaks.
• Reported outcomes:
  • First trial: bottom string breaks (contrary to some expectations).
  • Second trial: top string breaks.
  • Final “decisive” test (assigned to a student): bottom string breaks.
• Point emphasized: students’ intuition can fail—setup/force distribution and/or experimental details influence which string breaks first.

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List of researchers or sources featured

• Galileo Galilei (law of inertia, quoted/paraphrased)
• Isaac Newton (quoted from Principia)
• Albert Einstein (special relativity invoked for (v \sim c))
• Walter Lewin (lecturer demonstrating examples)
• Hero (Greek legend; referenced for “Hero’s engine” historical origin)
• Aphrodite (mythological context for Hero)
• Leander (mythological context for Hero)
• MIT (mentioned as where he prepared the device; not as a researcher)