2026 2학기 물리이론반 1-1 평형과 안정성 이론영상 p15~27

Main ideas / lessons

1) From force equilibrium to rotational equilibrium

• Previously, the video covered force equilibrium:
  • (\sum F = 0) (net force is zero) so the object does not accelerate.
  • For symmetric situations (e.g., equal forces left/right or top/bottom), forces cancel.
• Now it extends to objects that can rotate because they have size and forces can be applied at different points.

2) When equal opposite forces still cause rotation

• Even if two opposite forces are equal in magnitude and “cancel” in net force ((\sum F=0)), rotation can occur if they act at different positions relative to the rotation axis.
• Example concept:
  • Forces applied to opposite ends of a disk/rod can produce torques that cause clockwise rotation (depending on geometry).

3) Definition of torque and torque equilibrium

• The video introduces torque (rotational effect of a force).
• Rotational equilibrium condition:
  • (\sum \tau = 0) → torques clockwise and counterclockwise balance → no net rotation.
• Key qualitative definition:
  • Torque depends on:
    • Force magnitude (F)
    • Lever arm (r): perpendicular distance from the axis to the line of action of the force
    • (In general) only the component perpendicular to the lever arm creates torque.

4) Lever-arm dependence: why door handles are far from hinges

• If the same force is applied:
  • Smaller lever arm → smaller torque → harder to rotate
  • Larger lever arm → larger torque → easier rotation
• Practical examples: door handles, wrenches, tools.

5) Computing torque direction and magnitude

• Direction rule:
  • Torque direction is determined by whether the force tends to rotate the object clockwise or counterclockwise about the chosen axis.
• Magnitude rule emphasized repeatedly:
  • (\tau \propto F \times r)
• Special case emphasized:
  • If a force is applied parallel to the radius vector (i.e., its line of action is aligned with the axis-to-point segment), it can produce zero torque because the perpendicular lever arm is zero.

6) Choosing the axis to simplify torque calculations

• “Method skill”:
  • When calculating torque equilibrium, choose an axis.
  • A force applied at the axis produces zero torque (because (r=0)), so it can be ignored in the torque sum.
• This is used to reduce unknown-force terms.

7) Seesaw / fulcrum stability and required force-distance balance

• Example of equilibrium on a seesaw:
  • If one side is heavier, the other must compensate via force-distance (torque) balance.
  • Condition described:
    • Torque from side A + torque from side B must cancel (equal magnitude, opposite direction).
• Proportional reasoning:
  • If forces are in ratio (F_A:F_B), then lever arms must be in the inverse ratio to balance.

8) “Center of mass / center of gravity” as the torque-neutral location

• The center of mass (COM) is described as the point such that if you support the system there (as a pivot/axis), the net torque due to gravity becomes zero.
• For single-support cases:
  • The support must be located at the COM; otherwise the object tips.
• For two supports:
  • Stability requires COM to lie between the supports.
  • If COM shifts outside the supports’ span → collapse (tipping) occurs toward the side with less support.

9) Center-of-mass shift when a person/weight moves

• When one mass moves, COM moves accordingly.
• Approach described:
  • After movement, re-evaluate the torque balance using the new COM position.
  • Collapse occurs when the shifted COM passes the boundary (e.g., directly above one support).
• A proportional idea appears:
  • COM shift depends on the moved mass fraction of the total mass.

10) Multi-force / multi-physics examples solved using equilibrium

The latter part repeatedly applies:

• (\sum F = 0) (vertical force balance)
• (\sum \tau = 0) (torque balance about a chosen axis)
• COM and lever-arm reasoning

Used to solve numerical problems about:

• rods with masses at distances from fulcrums,
• doors and hinges,
• pulleys / axles and tensions,
• hanging masses via strings with different lever arms,
• stability thresholds for tipping.

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Method / instruction-style content (detailed bullets)

A) Steps for static equilibrium of a rotating object

• Step 1: Choose a coordinate/axis of rotation
  • Pick the rotation axis about which you will compute torque.
  • Advantage: if a force acts through the chosen axis, its torque is zero.
• Step 2: Write force equilibrium (if applicable)
  • Use vertical/horizontal components as needed:
    • (\sum F = 0)
  • Commonly: upward support forces (or tensions) equal total downward weights.
• Step 3: Write torque equilibrium
  • Compute torques from each force about the chosen axis:
    • (\sum \tau = 0)
  • For each torque:
    • determine direction (clockwise/counterclockwise),
    • compute lever arm (r) = perpendicular distance from axis to force line of action,
    • use (\tau = F \cdot r) (with the correct perpendicular-component concept).
• Step 4: Set up proportional/inverse relationships if symmetry or multiple equal forces are given
  • If (\tau_A=\tau_B):
    • (F_A r_A = F_B r_B)
  • So if (F_A/F_B) is known, then (r_A/r_B) is the inverse ratio.

B) Rules for “when torque is zero”

Torque is zero if:

• the force is applied at the axis ((r=0)),
• or the force is parallel to the radius/line from axis to point (perpendicular lever arm is zero).

C) Stability rules using COM (center of mass)

• Single support (one fulcrum/string contact):
  • Support point must coincide with COM for (\sum \tau = 0).
  • Otherwise the object tips.
• Two supports:
  • COM must lie between the two support points to remain stable.
  • If COM moves beyond either support:
    • torque no longer balances,
    • the system collapses toward that side.

D) Center-of-mass shift logic when one part moves

• When a mass moves by distance (x):
  • the COM shifts by an amount proportional to that mass relative to total mass.
• Collapse boundary occurs when COM reaches the support-line limit (edge of stability region).

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Speakers / sources featured

• No specific named speakers are clearly identifiable from the subtitles (the narration appears to be one instructor/teacher).
• Primary source: the video titled “2026 2학기 물리이론반 1-1 평형과 안정성 이론영상 p15~27” with an unnamed instructor narrator.