Relative Velocity Lecture 11 ME 231: Dynamics Question of the Day The velocity of the cart is 4 ft/s to the right. Determine the angular speed N (in rpm’s) of the wheel so that point A on the top of the rim has a velocity equal to zero. ME 231: Dynamics Outline for Today # Question ofof the dayday # Relative velocity due to rotation # Interpretation of vA = vB + vA/B # Solution of relative-velocity equation # Answer your questions! ME 231: Dynamics Recall: Relative Motion rA r?B rA/ B v A r?A rB rA/ B a A ?v A rA rB rA/ B # Absolute position of B is defined in an inertial coordinate system X-Y # Attach a set of translating (non-rotating) axes x-y to particle B and define the position of A # Define position of “A relative to B” (“A/B”) in x-y ME 231: Dynamics Relative Velocity Due to Rotation # Movement in two parts # First, body translates rB to parallel position rA rB rA/ B # Second, body rotates about From translating (non-rotating) B’ through axes x’-y’ attached to point B’, angle the remaining motion is a simple rotation about B’ giving rA/B ME 231: Dynamics Relative Velocity Due to Rotation Relative velocity as a scalar rA/ B vA/ B lim t 0 t r lim t 0 t r r r r A B A/ B …as a vector v A v B v A/ B Dividing by t v A/ B 2r ME 231: Dynamics Interpretation of Relative-Velocity Equation Translational Rotational portion portion 90º v 2r v B A/ B v A/ B v A v B v A/ B v A v B ME 231: Dynamics Outline for Today # Question ofof the dayday # Re Relativelative vevelocitylocity ddueue to rotationrotation # InterpretationInterpretation ofof vA = vB + vA/BA/B # Solution of relative-velocity equation # Answer your questions! ME 231: Dynamics Solution of Relative-Velocity Equation: Case #1 C v S Scalar-Geometric v r r D O T 2 m/s A /O O OE r U 2 2 2 vA vA /O vO 2vA /O vO cos120 2 2 2 vA 2 3 223 cos120 v 4.36 m/s A v A/O v A 2 m/s 60º r0 vO 3 m/s 2 v v v 10 rad/s A O A/O ME 231: Dynamics Solution of Relative-Velocity Equation: Case #2 Vector vA vO vA /O vO r0 i j k v A 3i 0 0 10 3i 1.7j i 4i 1.7j m/s 0.17 0.1 0 v v 4.36 m/s A/O A v A r0 vO 30º 3 m/s 2 v v v 10 rad/s A O A/O ME 231: Dynamics Relative Velocity: Exercise A mechanic “walks” a two-tire unit that rolls without slipping at constant speed v. The radius of both tires is r. Determine the velocities of points A, B, C, and D. ME 231: Dynamics Outline for Today # Question ofof the dayday # Re Relativelative vevelocitylocity ddueue to rotationrotation # InterpretationInterpretation ofof vA = vB + vA/BA/B # SolutionSolution of relative-velocityrelative-velocity eequationquation # Answer your questions! ME 231: Dynamics For Next Time… # Complete Homework #4 due on Thursday (9/20) # Read Chapter 6, Section 6.2 ME 231: Dynamics.