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# l16anno - Plane Motion of a Rigid Body Points P and Q are...

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Plane Motion of a Rigid Body Points P and Q are fixed on the rigid body B that is in plane motion relative to the x-y plane that is fixed in the reference frame T

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Rigid body: distance between any two points is constant Plane Motion: All points move parallel to the x-y plane All points P ’ located at r OP + z k are identified by point P, etc . x z ' P P y , ' P P x y OP r OP r
cos sin ) sin cos ) cos si ) ( ( n ( OQ OP PQ OQ OP PQ Q P PQ PQ PQ PQ PQ PQ P P Q P Q Q r r r θ θ θ θ θ θ θ θ θ θ = + = + + + = × + = = + = = × = + × = r r r r r r v v r r i j r i j k i j k v r k v r ω ω ± ± ± ± ± ± ± ± ± Velocity Angular Velocity ω

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θ = ω k ± Angular velocity of B. Angular velocity is independent of the points P and Q; it is a property of the motion of B P S R Q θ θ ' 0 ' Q P PQ P PQ S R RS R RS θ θ φ θ θ φ θ θ θ θ = + = + = + = + × = + × = + × = + × = v v k r v r v v k r v ω ω r ± ± ± ± ± ± ± constant φ = ω θ S , R P Q
2 is th e an g u lar accel ( ) ( ) ( (co s sin )) ( ( sin co s )) ( co s s ( ) eratio n Q P P Q P Q P P Q P P Q Q P P P Q P Q P Q P Q P Q P Q P Q Q P Q Q r r r θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ × = × = + × = × = × × = + × = + × + × × + = × = + + = = × × × × + a a α r v v ω r v k r v v k r k r ω ω ω ω r k k r k k i j k i r ω j i k r α r ±

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