Chapter 12.
Chapter 12. Equilibrium Equilibrium
• Equilibrium
– Σ F = 0
– Σ τ = 0
τ = Iα (1/2)Iω2
I α ω θ
회전운동
(angular motion)
N J kg m/s2
m/s m
N.m F = ma
운동방정식 (Newton’s 2nd)
J (1/2)mv2
운동에너지 (KE)
kg.m2 관성 (inertia) m
1/s2 가속도 (acceleration) a
1/s 속도 (velocity) v
- 변위 (displacement) x
병진운동 (linear motion)
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
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
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
pivot
• 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
Equilibrium Example
A 50 kg diver stands at the end of a 4.6 m diving board.
Neglecting the weight of the board, what is the forces on the pivots?
1) Choose Axis of rotation 2) Σ τ = 0 Rotational EQ
F1 (1.2) – mg (4.6) = 0 F1 = 4.6 (50 *9.8) / 1.2
F1 = 1880 N 1.2 m 3.4 m
Summary
• Equilibrium
Σ F = 0 Σ τ = 0
• Can choose any axis.