KINEMATICS_OF_RIGID_BODIES

KINEMATICS_OF_RIGID_BODIES - instant as you determine the...

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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 ϖ 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 ): 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: F F ROTATION OF A SLAB: R R UNIFORM ROTATION: U U UNIFORMLY ACCELERATED ROTATION: U U velocities IN PLANE MOTION (point A translates!): v v INSTANTANEOUS CENTER OF ROTATION: the point about which you can assume a body is rotating at a given
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Unformatted text preview: 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 pp ACCELERATION IN PLANE MOTION: AA Noncentroidal Rotation G tG r a = 2 G ntG r a = Moment of Inertia, Radius of Gration 2 G G o mr I I + = 2 G G mk I = Rolling Motion balanced disk Rolling, no slipping N friction s μ ≤ ; 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 ) ( ) ( / / → → → → + + =...
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