PHY 101 1nd Edition Lecture 22 Outline of Last Lecture I Chapter 8 Rotational Equilibrium and Dynamics II 8 1 Torque a Force vs Torque III 8 2 Torque and Rotational Equilibrium Outline of Current Lecture IV Two Conditions for Equilibrium V 8 3 Center of Gravity VI 8 4 Solving Equilibrium Problems VII Axis of Rotation Current Lecture Two Conditions of Equilibrium To ensure mechanical equilibrium we need to have rotational equilibrium and translational equilibrium Translational Equilibrium the net external force must be equal to zero o F 0 Rotational Equilibrium the net external torque must be equal to zero o 0 When calculating the total torque it is important to o Select an axis o Find all forces and their torques 8 3 Center of Gravity Center of gravity if the torque exerted by gravitational force has to be considered all of the weight of the object has to be considered as if it were at a single point The center of gravity of a system of masses can be defined by o Xcg mixi mi m1x1 m1 m2x2 m2 o Ycg miyi mi m1y1 m1 m2y2 m2 The center of gravity of a uniform object is located at its geometric center These notes represent a detailed interpretation of the professor s lecture GradeBuddy is best used as a supplement to your own notes not as a substitute 8 4 Solving Equilibrium Problems Draw a diagram of the system include coordinates and choose a rotation axis Isolate the object being analyzed draw a free body diagram including all the external forces acting on it Apply the Second Condition of Equilibrium 0 Apple the First Condition of Equilibrium F 0 Solve the resulting simultaneous equations for all the unknowns Axis of Rotation If an object is in equilibrium it does not matter where you put the axis of rotation for calculating the net torque Often the problem will provide a convenient location for the axis otherwise you must specify its location You must maintain that choice consistently throughout the problem
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