ME 242 Lecture 31 04.22

ME 242 Lecture 31 04.22 - H O = H G + r G / O mv G For...

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1 ME 242 Dynamics April 23, 2009 Eric Wang Today’s Key Concepts Chapter 7: Kinetics of Rigid Bodies Linear Impulse-Momentum Angular Impulse-Momentum Recall: Rigid Body General 2D Motion Kinematics Kinetics a B = a A + α × r B / A + ω × ( × r B / A ) v B = v A + × r B / A F = ma G M G = I G ˙ ˙ θ b 3 M A = I G ˙ ˙ b 3 + r G / A × ma G M A = I A ˙ ˙ b 3 + r G / A × ma A Linear Impulse-Momentum for a Rigid Body L = mv G • Linear Momentum • Impulse-Momentum LI 1 2 = Σ F dt t 1 t 2 = ( mv G ) 2 ( mv G ) 1 Example (prob. 7.4.4) Given : m A = 16 kg, r = 0.5m, m B =8 kg, F= 10 N, A rolls w/o slipping B slides on frictionless surface Find : ω A after 5s if v B =3.75 m/s FBD’s m B g m A g N 1 N 2 F f F f N 2
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2 Before & After At rest v O v B ω A Impulse-Momentum (horizontal component) Impulse-Momentum (horizontal component) Angular Momentum for 2D motion • Angular Momentum for 2D motion AI G 1 2 = M G dt t 1 t 2 = ( H G ) 2 ( H G ) 1 H G = I G ˙ θ b 3 • Angular Impulse-Momentum Angular Momentum about a fixed point O
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Unformatted text preview: H O = H G + r G / O mv G For rotation about a fixed point O: AI O 1 2 = M O dt t 1 t 2 = ( H O ) 2 ( H O ) 1 H O = I O b 3 Example (prob. 7.4.13) Given: =0.65, r = 3.5cm, m = 0.11kg and initial v G =5 m/s, = 20 rad/s Find: how far does it go before transitioning to rolling w/o slip? 3 FBD mg N F f Before and After 2 v G 1 v G 2 1 Angular Impulse Momentum Angular Impulse Momentum Linear Impulse Momentum Combine Equations 4 Finish it up Take Home Points Linear Momentum Linear Impulse Angular Momentum Angular Impulse L = mv G LI 1 2 = F dt t 1 t 2 = ( mv G ) 2 ( mv G ) 1 AI G 1 2 = M G dt t 1 t 2 = ( H G ) 2 ( H G ) 1 H G = I G b 3...
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This note was uploaded on 09/19/2009 for the course ME 242 taught by Professor Kam during the Spring '06 term at Nevada.

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ME 242 Lecture 31 04.22 - H O = H G + r G / O mv G For...

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