Principal Axis Theorem and 3- Dimensional Rotation 8.01 W13D1Next Reading Assignment: W13D2 Young and Freedman: 10.7Rules to Live By: Angular Momentum and Torque 1) About any fixed point S 2) Independent of the CM motion, even if and are not parallel ,S about cm of cm about cm s cm total cmr m v= + = + ×L L L L τS=τS ,iext=dLSdti∑about cmabout cmddtτ=Labout cmLωConcept Question: Chasles’ Theorem The displacement of any rigid body can be described by the displacement of the center of mass and a rotation about some axis passing through the center of mass 1. This is not true. 2. This is always true. 3. This is only true for small (differential displacements) 4. It is only true if the rotation is about a symmetry axis. .Chasles’ Theorem: AnswerConcept QuestionConcept Question: AnswerConcept QuestionConcept Question: AnswerConcept QuestionConcept Question: AnswerDemo Torque on a Rotating PlateTorque and Time Derivative of Angular Momentum Torque about S is equal to the time derivative of the angular momentum about S If the magnitude of the angular momentum is constant then the torque can cause the direction of the angular momentum to change extSSSddt=Lτ τSSext=ωLS
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