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chapter8 - Chapter 8 Rotational Equilibrium and Rotational...

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Chapter 8 Chapter 8 Rotational Equilibrium and Rotational Dynamics

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Wrench Demo Wrench Demo
Torque Torque Torque, τ , is tendency of a force to rotate object about some axis F is the force d is the lever arm (or moment arm) Units are Newton-m τ = Fd

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Torque is vector quantity Torque is vector quantity Direction determined by axis of twist Perpendicular to both r and F Clockwise torques point into paper. Defined as negative Counter-clockwise torques point out of paper. Defined as positive
Non-perpendicular forces Non-perpendicular forces Φ is the angle between F and r τ = Fr sin f

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Torque and Equilibrium Torque and Equilibrium Forces sum to zero (no linear motion) Torques sum to zero (no rotation) Σ F x = 0 and S F y = 0 Σ τ = 0
Meter Stick Demo Meter Stick Demo

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Axis of Rotation Axis of Rotation Torques require point of reference Point can be anywhere Use same point for all torques Pick the point to make problem least difficult
Example 8.1 Example 8.1 Given M = 120 kg. Neglect the mass of the beam. a) Find the tension in the cable b) What is the force between the beam and the wall a) T=824 N b) f=353 N

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Another Example Another Example Given: W=50 N, L=0.35 m, x=0.03 m Find the tension in the muscle F = 583 N x L W
Center of Gravity Center of Gravity Gravitational force acts on all points of an extended object However, it can be considered as one net force acting on one point, the center-of-gravity, X. Weighted Average ( m i g ) x i i = =   =

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Example 8.2 Example 8.2 Fig 8.12, p.228 Slide 17 Given: x = 1.5 m, L = 5.0 m, w beam = 300 N, w man = 600 N Find: T x L T = 413 N
Example 8.3 Example 8.3 Consider the 400-kg beam shown below.

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chapter8 - Chapter 8 Rotational Equilibrium and Rotational...

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