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Chapter 12

# Chapter 12 - Announcements Test 2 scores are posted on...

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Announcements • Test 2 scores are posted on E-learning • Distribution 0 2 4 6 8 10 12 14 16 18 1 2 3 4 5 6 7 8 9 10 11 12 Series1

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Chapter 12 Equilibrium and elasticity Part 1

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Equilibrium A body is in equilibrium if: Conditions for equilibrium: The net force acting on the body is ZERO The net torque acting on the body is ZERO The COM moves with a constant speed on a straight line and the rotation of a rigid body is at a constant rate (constant angular velocity) r F net = r F = 0 r τ net = r τ = 0 r P = constant r L = constant r F net = d r P dt = 0 r τ net = d r L dt = 0

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Static Equilibrium In static equilibrium the body does not move No translation! No rotation! Conditions for static equilibrium (the same): The net force acting on the body is ZERO The net torque acting on the body is ZERO This should be true for any part of of the system and for any axis of rotation. r P = constant = 0 r L = constant = 0
A closer look! Balance of the forces ( all as if applied at the COM ) Balance of the torque ( around any axis of rotation ) r F net = r F = 0 r τ net = r τ = 0 F net , x = F x = 0 F net , y = F y = 0 F net , z = F z = 0 τ net , x = τ x = 0 τ net , y = τ y = 0 τ net , z = τ z = 0 r F 1 r F 2 r F 3 r F 1 r r 1 r F 2 r F 3 r r 2 r r 3

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Simple case : co-planar forces
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