Lecture 26

Lecture 26 - Last Meeting Physics 231 General University...

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Physics 231 General University Physics Lecture 26 Lecture 9 1 Last Meeting ± Moment of Inertia ± Kinetic Energy ± Rolling Lecture 9 2 Today ± Torque ² Rotational Analog of Force Lecture 9 3 Rotational Dynamics: Particle Moving in a Circle ± Consider a particle of mass m rotating in a circle of radius r under the influence of tangential force, F t , and centripetal force ± The tangential force provides a tangential acceleration: F t = ma t ± The tangential acceleration is related to the angular acceleration, a t = r α , so F t = mr Lecture 9 4 Particle Moving in a Circle (cont.) ± Then ( F t r ) = ( mr 2 ) ± Since we recognize I=mr 2 as the moment of inertia of the particle, this suggests that we write ± where we define the “torque” I τ = t rF Lecture 9 5 Torque & Angular Acceleration Particle Moving in a Circle (Cont.) ± Compare ± to ± Correspondence: I = Fm a = a mI F
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Lecture 9 6 Dictionary v ω a α mI F τ 2 1 2 Km v = 2 1 2 KI = net Fm a = G G net I = Translation Rotation Lecture 9 7 Torque ± Demo: Model Door with Spring Meter ± Demo: Rope on Door Handle Lecture 9 8 Torque ( ) sin sin t rF rF r F τφ φ == = “lever arm” r d=rsin φ φ φ F t =Fsin φ F O Lecture 9 9 Lever Arm ± Torque, , is the tendency of a force to rotate an object about some axis ² Torque is a vector ² = r (F sin φ) = F ( r sin φ) = F d ± F is the force ± is the angle the force makes with the radius ± d is the moment arm or lever arm Lecture 9 10 Lever arm (cont.) ± The lever arm, d , is the
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This note was uploaded on 11/16/2010 for the course PHY 231 taught by Professor Ellis during the Spring '08 term at Kentucky.

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Lecture 26 - Last Meeting Physics 231 General University...

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