16notes - alpha and Ag are independent. Hence, a ball...

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Forces for plane motion Forces will cause translation and rotation If body is unconstrained, the center of mass will go through translation and other points on body will go through general plane motion Newton’s law should be used only about the center of mass G for plane motion Have choose a reference point for body like G Translation Motion Fx=mabar, Fy=mabar Mg=0, alpha is zero Since M=0, can take moment from any point like statics
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Centroidal Motion Fx and Fy are zero, abar is zero, Moment =Ibar*alpha
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Unconstrained The linear acceleration abar of the center of mass is totally independent of alpha
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Suppose now L becomes 2L, notice only alpha changes and not abar. Hence, the reason for this motion is unconstrained. Part b) accelerations
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If the ball slips, then Acx doesn’t equal to zero. So even if alpha=0, Ag doesn’t equal to zero. Hence
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Unformatted text preview: alpha and Ag are independent. Hence, a ball sliding and rotating performs an unconstrained plane motion. Ball rolls without slipping then Acx=0 and Ag=alpha*r. Now there is a relationship between Ag and alpha making them dependent. This motion is constrained. Ball slips in this problems so use case A. • In constrained motion, a definite relation exists between the components of acceleration abar of the mass center and alpha • Pure rotation is tangential and normal equations, abar=alpha*rbar +w^2*rbar • If we take moment about pin O, it is Mo=Io*alpha • We can now take moment about O in constrained case as well Summary: Ag doesn’t depend on alpha so unconstrained motion...
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16notes - alpha and Ag are independent. Hence, a ball...

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