Chapt 8 - Rotational Motion and Equilibrium Chapter 8 Translational and Rotational Motion The most general motion of a rigid body can be analyzed

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1 Rotational Motion and Equilibrium Chapter 8 Translational and Rotational Motion The most general motion of a rigid body can be analyzed as a translation of the center of mass plus a rotation about its center of mass. Rolling Without Slipping
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2 Rolling Without Slipping Linear velocity of the center of mass is: v CM = (s f – s i )/ t = s/ t But s = r ∆θ b v CM = r( ∆θ / t) Thus v CM = r ϖ Acceleration of the center of mass is: a CM = v CM / t = r ∆ϖ / t a CM = r α Example 8-1 2 v CM v CM R = 0.12m V CM = 0.10m/s t = 2.0s Find ϖ : ϖ = v CM /r = [0.10m/s]/0.12m = 0.083 rad/s Find θ: θ = ϖ∆ t = [0.083rad/s][2.0s] = 1.7 rad ( π /2 = 1.57 rad) Newton’s 2’ nd Law of Motion Applied to Rotational Motion c A force is required to produce a change in rotational motion. c But the rate of change of motion depends not only on the magnitude and direction of the force, but also on the so-called moment arm c The moment arm is the perpendicular distance from the line of force to the axis of rotation
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3 Definition of Moment Arm and Torque c The moment arm, r , is the perpendicular distance from the extension of the force vector to the axis of rotation. c r = r·sin(θ) c Torque is defined to be a force “F” acting through a moment arm “r τ ≡ F·r = F·r·sin( θ ) c θ = angle between r and F c SI Units are N·m c US Units are ft·lb c Torque results in rotational motion F r r Figure 8-3 Torque and Moment Arm More Definitions c Torque is a vector quantity c The direction is perpendicular to the plane determined by the moment arm and the force c The torque is taken to be positive if the turning tendency of the force is counterclockwise , c If a torque produces a clockwise turning tendency, that torque is said to be negative
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More About Torque c The net torque is the sum of all the torques produced by all the forces c τ net = τ 1 + τ 2 + τ 3 + … τ n c Remember to account for the direction of the tendency for rotation c Counterclockwise torques are positive c Clockwise torques are negative Example 8-2 c r = 0.04 m F = 600 N c r = r . cos(30
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This note was uploaded on 01/05/2012 for the course PHYS 1401 taught by Professor Jamesr.boyd during the Spring '09 term at Collins.

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Chapt 8 - Rotational Motion and Equilibrium Chapter 8 Translational and Rotational Motion The most general motion of a rigid body can be analyzed

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