ME 242 Lecture 32 04.24

ME 242 Lecture 32 04.24 - 1 ME 242 Dynamics Eric Wang...

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Unformatted text preview: 1 ME 242 Dynamics April 24, 2009 Eric Wang Today’s Key Concepts Chapter 7: Kinetics of Rigid Bodies • Work-Energy • In-class experiment • In-class demonstration • Example Recall: Rigid Body General 2D Motion Kinematics Kinetics a B = a A + α × r B / A + ω × ( ω × r B / A ) v B = v A + ω × r B / A ∑ F = ma G ∑ M G = I G ˙ ˙ θ b 3 ∑ M A = I G ˙ ˙ θ b 3 + r G / A × ma G ∑ M A = I A ˙ ˙ θ b 3 + r G / A × ma A Recall: Impulse-Momentum • Linear Momentum • Linear Impulse • Angular Momentum • Angular Impulse L = mv G LI 1 − 2 = Σ 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 ˙ θ b 3 Rigid Bodies Kinetic Energy Translational KE Rotational KE KE = 1 2 mv G 2 + 1 2 I G ω 2 Often, v G and ω will be related via the rigid body equations Work-Energy for Rigid Bodies KE 1 +PE 1 + W nc 1 − 2 = KE 2 +PE 2 PE = − F c ∫ • ds W nc = F nc • ds ∫ KE = 1 2 mv G 2 + 1 2 I G ω 2 Typically gravity &...
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ME 242 Lecture 32 04.24 - 1 ME 242 Dynamics Eric Wang...

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