Static Equilibrium

# Static Equilibrium - Chapter 12 Static Equilibrium and...

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1 Chapter 12 Chapter 12 Static Equilibrium and Elasticity c There are two necessary conditions for equilibrium c The resultant external force must equal zero: Σ F = 0 b This is a statement of translational equilibrium b The acceleration of the center of mass of the object must be zero when viewed from an inertial frame of reference c The resultant external torque about any axis must be zero: Στ = 0 b This is a statement of rotational equilibrium c For rotation, Στ = I α b For rotational equilibrium, Στ = 0 c Need the angular acceleration of the object to be zero Conditions for Equilibrium

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2 Static vs. Dynamic Equilibrium Static vs. Dynamic Equilibrium c In this chapter, we will concentrate on static equilibrium b The object will not be moving b v CM = 0 and ω = 0 c Dynamic equilibrium is also possible b The object would be rotating with a constant angular velocity b The object would be moving with a constant v CM c In either case, the Στ = 0 c There are two necessary conditions for equilibrium The resultant external force must equal zero Σ F = 0 (translational equilibrium) The resultant external torque about any axis must be zero: Στ = 0 (rotational equilibrium) b Σ F x = 0 b Σ F y = 0 b Σ τ z = 0 Equilibrium Equations Equilibrium Equations
3 Center of Mass Center of Mass c An object can be divided into many small particles b Each particle will have a specific mass and specific coordinates c The x coordinate of the center of mass will be c Similar expressions can be found for the y and z coordinates i i i CM i i m x x m = Center of Gravity Center of Gravity c All the various gravitational forces acting on all the various mass elements are equivalent to a single gravitational force acting through a single point called the center of

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Static Equilibrium - Chapter 12 Static Equilibrium and...

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