Relative Velocity Due to Rotation

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Relative Velocity Due to Rotation

Relative VelocityLecture 11ME 231: Dynamics


Outline for Today Question of the day Relative velocity due to rotation Interpretation of v A = v B + v A/B Solution of relative-velocity equation Answer your questions!ME 231: Dynamics


Recall: Relative Motion? vr?rA r?B rA/BvA A rB rA/BaA A rA rB rA/BAbsolute position of B is defined in an inertialcoordinate system X-YAttach a set of translating (non-rotating) axes x-y toparticle B and define the position of ADefine position of “A relative to B” (“A/B”) in x-yME 231: Dynamics


Relative Velocity Due to Rotation Movement intwo parts First, bodytranslatesr B to parallelposition Second, bodyrotates aboutB’ throughangle r r rA B A/BFrom translating (non-rotating)axes x’-y’ attached to point B’,the remaining motion is a simplerotation about B’ giving r A/BME 231: Dynamics


Relative Velocity Due to RotationRelative velocityas a scalarvAAB lim r // t 0 tr lim t 0 t rBr r rA B A/B…as a vectorvA/ B rvvvA B A/BDividing by tME 231: Dynamics


Interpretation of Relative-Velocity EquationTranslationalportionRotationalportion90ºv BvA/ BrvvvA B A/Bv A/ Bv Av BME 231: Dynamics


Outline for Today Question of the day Relative velocity due to rotation Interpretation of v A = v B + v A/B Solution of relative-velocity equation Answer your questions!ME 231: Dynamics


Solution of Relative-Velocity Equation: Case #1Scalar-Geometricv 2 2A v A /Ov 2 A 2 2 3 2 22 3 cos120v A 4.36 m/s v 2 O 2v A /Ov A/O2 m/s 60ºr 010 rad/sv A /O r O r v OO rv O cos1203 m/sv Ov Av 2 m/svvA O A/OME 231: Dynamics


Solution of Relative-Velocity Equation: Case #2Vectorv A v O v A /O v O r 0i j kvA 3i 0 0.1700.110 3i1.7ji 4i1.7j0m/sv A 4.36 m/sv A/Ov Ar 030º10 rad/s3 m/sv OvvvA O A/OME 231: Dynamics


Relative Velocity: ExerciseA mechanic “walks” a two-tire unit that rollswithout slipping at constant speed v. The radiusof both tires is r.Determine the velocitiesof points A, B, C, and D.ME 231: Dynamics


Outline for Today Question of the day Relative velocity due to rotation Interpretation of v A = v B + v A/B Solution of relative-velocity equation Answer your questions!ME 231: Dynamics


For Next Time… Complete Homework #4 due onThursday (9/20) Read Chapter 6, Section 6.2ME 231: Dynamics

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