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lecturenotes-March17

# lecturenotes-March17 - Ch 12 Equilibrium Equilibrium when...

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Unformatted text preview: Ch. 12: Equilibrium Equilibrium when: Remember Newton’s 2 nd law: F net = F i ∑ = m a = d P dt τ net = τ i ∑ = I α = d L dt P = constant L = constant 1) Linear Momentum of its center of mass is constant 2) Angular Momentum about any point is constant P = L = Static Equilibrium when: a = = α d P dt = = d L dt ⇒ v com = ⇒ ω = Checkpoint 12-1 The fgure gives an overhead view oF a uniForm rod in static equilibrium. a) Can you fnd the magnitudes oF ¡ 1 and ¡ 2 by balancing the Forces? b) IF you wish to fnd the magnitude oF ¡ 2 by using a single equation, where should you place a rotational axis? 1) Draw a Free-body diagram showing all Forces acting on body and the points at which these Forces act. 2) Draw a convenient coordinate system and resolve Forces into components. 3) Using letters to represent unknowns, write down equations For: ∑ ¡ x =0, ∑ ¡ y =0, and ∑ ¡ z =0 4) ¡or ∑ τ = 0 equation, choose any axis perpendicular to the xy plane. But choose judiciously! Pay careFul attention to determining lever arm and sign! [For xy-plane, ccw is positive & cw is negative] 5) Solve equations For unknowns. Checkpoint 12-1 The fgure gives an overhead view oF a uniForm rod in static equilibrium. a) Can you fnd the magnitudes oF ¡ 1 and ¡ 2 by balancing the Forces? b) IF you wish to fnd the magnitude oF ¡ 2 by using a single equation, where should you place a rotational axis? Problem 12-7 1) Draw a free-body diagram showing all forces acting on body and the points at which these forces act. 2) Draw a convenient coordinate system and resolve forces into components. 3) Using letters to represent unknowns, write down equations for: ∑ F x =0, ∑ F y =0, and ∑ F z =0 4) For ∑ τ = 0 equation, choose any axis perpendicular to the xy plane. But choose judiciously! Pay careful attention to determining lever arm and sign! [for xy-plane, ccw is positive & cw is negative] 5) Solve equations for unknowns. A diver of weight 580 N stands on the end of a 4.5 m diving board of negligible mass. The board is attached to two pedestals 1.5 m apart. What is the magnitude and direction of the force on the board at the left and right pedestals? Problem 12-7 A diver of weight 580 N stands on the end of a 4.5 m diving board of negligible mass. The board is attached to two pedestals 1.5 m apart. What is the magnitude and direction of the force on the board at the left and right pedestals? Sample Problem A uniform beam of length L and mass m is at rest with its ends on two scales. A uniform block, with mass M is rest on the beam, with its center a distance L/4 from the beam’s end. What do the scales read?...
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lecturenotes-March17 - Ch 12 Equilibrium Equilibrium when...

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