Relative Velocity Due to Rotation
Relative Velocity Due to Rotation
Relative Velocity Due to Rotation
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
<strong>Relative</strong> <strong>Velocity</strong>Lecture 11ME 231: Dynamics
Outline for Today Question of the day <strong>Relative</strong> velocity due <strong>to</strong> rotation Interpretation of v A = v B + v A/B Solution of relative-velocity equation Answer your questions!ME 231: Dynamics
Recall: <strong>Relative</strong> 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 <strong>to</strong>particle B and define the position of ADefine position of “A relative <strong>to</strong> B” (“A/B”) in x-yME 231: Dynamics
<strong>Relative</strong> <strong>Velocity</strong> <strong>Due</strong> <strong>to</strong> <strong>Rotation</strong> Movement intwo parts First, bodytranslatesr B <strong>to</strong> parallelposition Second, bodyrotates aboutB’ throughangle r r rA B A/BFrom translating (non-rotating)axes x’-y’ attached <strong>to</strong> point B’,the remaining motion is a simplerotation about B’ giving r A/BME 231: Dynamics
<strong>Relative</strong> <strong>Velocity</strong> <strong>Due</strong> <strong>to</strong> <strong>Rotation</strong><strong>Relative</strong> velocityas a scalarvAAB lim r // t 0 tr lim t 0 t rBr r rA B A/B…as a vec<strong>to</strong>rvA/ B rvvvA B A/BDividing by tME 231: Dynamics
Interpretation of <strong>Relative</strong>-<strong>Velocity</strong> EquationTranslationalportion<strong>Rotation</strong>alportion90ºv BvA/ BrvvvA B A/Bv A/ Bv Av BME 231: Dynamics
Outline for Today Question of the day <strong>Relative</strong> velocity due <strong>to</strong> rotation Interpretation of v A = v B + v A/B Solution of relative-velocity equation Answer your questions!ME 231: Dynamics
Solution of <strong>Relative</strong>-<strong>Velocity</strong> 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 <strong>Relative</strong>-<strong>Velocity</strong> Equation: Case #2Vec<strong>to</strong>rv 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
<strong>Relative</strong> <strong>Velocity</strong>: 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 <strong>Relative</strong> velocity due <strong>to</strong> 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
Change language