Equation_Sheet2

Equation_Sheet2 - Plane Motion of Rigid Bodies Forces and...

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Unformatted text preview: Plane Motion of Rigid Bodies: Forces and Accelerations Equations of motion for a rigid body G a m F → → = ∑ G H M • → → = ∑ Angular Momentum of a rigid body in plane motion → → = ω G G I H → → = → = • • α ω G G G I I H Plane motion of a rigid body. xG x a m F = ∑ ; yG y a m F = ∑ α G G I M = ∑ ; α o o I M = ∑ RATE OF CHANGE OF A VECTOR (with respect to a fixed frame-OXYZ and a rotating one- Oxyz (with Ω ): Q Q Q Oxyz OXYZ r r & r & r × Ω + = ) ( ) ( PLANE MOTION OF A PARTICLE RELATIVE TO A ROTATING FRAME: F P C F P P P C F P P P F P P P F P P P v acc Coriolis a frame rotating the to relative P of acc a frame rotating the with P of acc a acc absolute a a a a a frame rotating the to relative P of vel v frame rotating the with P of vel v vel absolute v v v v / / ' / ' / ' / ' 2 . . . . . . . r r r r r r r r r r r r r r r r × Ω = = = = = + + = = = = + = KINEMATICS OF RIGID BODIES TRANSLATION: all particles have the same velocities and accelerations at any given instant...
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Equation_Sheet2 - Plane Motion of Rigid Bodies Forces and...

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