Equation_Sheet2

Equation_Sheet2 - pp ACCELERATION IN PLANE MOTION: AA...

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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 = ϖ G G I H = = α G G G I I H Plane motion of a rigid body. xG x a m F = ; yG y a m F = G G I M = ; o o I M = RATE OF CHANGE OF A VECTOR (with respect to a fixed frame-OXYZ and a rotating one- Oxyz (with ): PLANE MOTION OF A PARTICLE RELATIVE TO A ROTATING FRAME: R KINEMATICS OF RIGID BODIES TRANSLATION: all particles have the same velocities and accelerations at any given instant a ROTATION ABOUT A FIXED AXIS: FF ROTATION OF A SLAB: RR UNIFORM ROTATION: UU UNIFORMLY ACCELERATED ROTATION: UU velocities IN PLANE MOTION (point A translates!): vv INSTANTANEOUS CENTER OF ROTATION: the point about which you can assume a body is rotating at a given instant, as you determine the velocities of the points of the body at that instant. v IC =0 ; v point/IC = ϖ r point/IC ; r point/IC v point/IC
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Unformatted text preview: pp ACCELERATION IN PLANE MOTION: AA Noncentroidal Rotation G tG r a = 2 G ntG r a = Moment of Inertia, Radius of Gyration 2 G G o mr I I + = 2 G G mk I = Rolling Motion balanced disk Rolling, no slipping N friction s ; G G r a = Rolling, slipping impending N friction s = ; G G r a = Rolling, slipping N friction K = ; and a G are independent Unbalanced disk o r a = n o G t o G o G a a a a ) ( ) ( / / + + = Plane Motion of Rigid Bodies: Energy Methods WORK-ENERGY Principle T 1 +U 1-2 = T 2 CONSERVATION OF ENERGY Principle T 1 +V 1 = T 2 +V 2 T= mv 2 + I 2 U 1-2 = r d F U 1-2 = Md U 1-2 =M( 2- 1 ) SYSTEM MOMENTA 1 + SYST. EXTERNAL IMPULSE 1-2 = SYSTEM MOMENTA 2 L= mv Linear impulse= dt F H = I Angular impulse dt M...
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This note was uploaded on 07/09/2011 for the course EGN 3311 taught by Professor Hudyma during the Fall '08 term at UNF.

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Equation_Sheet2 - pp ACCELERATION IN PLANE MOTION: AA...

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