Chapter 12.
Chapter 12. Equilibrium Equilibrium
• Equilibrium
– Σ F = 0
– Σ τ = 0
병진운동 (linear motion)
회전운동
(angular motion)
변위 (displacement) x m θ
ω α
I (1/2)Iω2
τ = Iα
- 속도 (velocity) v
m(r x v)
rad/s 가속도 (acceleration) a
m/s m/s2
kg J N
rad/s2
관성 (inertia) m kg.m2
운동에너지 (KE) (1/2)mv2 J
운동방정식 (Newton’s 2nd) F = ma N.m N.s
모멘텀 (momentum) mv J.s
Review of last lecture
Review of last lecture
Question
• A rod is lying on a table and has two equal but opposite forces acting on it. What is the net force on the rod?
A) Up B) Down C) Zero
• Will the rod move? A) Yes B) No
y Fx
Y direction: Σ F
y= ma
y+F – F = 0
Yes, it rotates!
Question
The picture below shows two people lifting a heavy log. Which of the two people is supporting the greatest weight?
1. The person on the left is supporting the greatest weight
2. The person on the right is supporting the greatest weight
3. They are supporting the same weight CORRECT
FL FR
L
Look at torque about center:
Στ = FR L – FL L/2 = 0
Equilibrium
• Conditions for Equilibrium
¾ Σ F = 0 Translational EQ (Center of Mass)
¾ Σ τ = 0 Rotational EQ
9Can choose any axis of rotation…. Choose Wisely!
Static Equilibrium and Center of Mass
Center of mass pivot
d
• Gravitational Force Weight = mg – Acts as force at center of mass
– Torque about pivot due to gravity τ = mgd – Object not in static equilibrium
∑∑
=
i i i
cm m
m r r
Center of mass pivot
d
W=mg
Torque about pivot ≠ 0 Not in equilibrium
Center of mass pivot
Torque about pivot = 0 Equilibrium
Static Equilibrium
Summary
• Equilibrium
Σ F = 0 Σ τ = 0
• Can choose any axis.
