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Published byGuillermo Doby Modified about 1 year ago

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Particle vs. Rigid-Body Mechanics What is the difference between particle and rigid-body mechanics? –Rigid-body can be of any shape Block Disc/wheel Bar/member Etc. Can determine motion of any single particle (pt) in body particle Rigid-body (continuum of particles)

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Types of Rigid-Body Motion Kinematically speaking… –Translation Orientation of AB constant –Rotation All particles rotate about fixed axis –General Plane Motion (both) Combination of both types of motion B A B A B A B A

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Kinematics of Translation Kinematics –Position –Velocity –Acceleration True for all points in R.B. (follows particle kinematics) B A x y rBrB rArA

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Rotation about a Fixed Axis – Angular Motion Point P travels in circular path (whether “disk” or not) Angular motion –Angular position, θ –Angular displacement, d θ Angular velocity ω =d θ /dt Angular Acceleration – α =d ω /dt r Axis of rotation

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Rotation about a Fixed Axis – Angular Motion Point P travels in circular path (whether “disk” or not) Angular motion –Angular position, θ –Angular displacement, d θ Angular velocity ω =d θ /dt Angular Acceleration – α =d ω /dt Angular motion Equations r Axis of rotation In solving problems, once know ω & α, we can get velocity and acceleration of any point on body!!! (next slide) (Or can relate the two types of motion if ω & α unknown )

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Rotation about a Fixed Axis – Motion of Point Point P travels in circular path Position of P –Defined by r If body rotates some d θ, then displacement is ds = r d θ –Velocity (tangent to path) –Acceleration (2 components) r v v ∆v∆v anan anan ∆v∆v a a atat anan

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Example Problem When the gear rotates 20 revolutions, it achieves an angular velocity of ω = 30 rad/s, starting from rest. Determine its constant angular acceleration and the time required. (F16-1, 3.58 rad/s 2, 8.38 s)

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Example Problem The gear A on the drive shaft of the outboard motor has a radius of r A = 0.5 in and the meshed pinion gear B on the propeller shaft has a radius r B = 1.2 in. Determine the angular velocity of the popular in t = 1.5 s, if the drive shaft rotates with an angular acceleration = (400t 3 ) rad/s 2, where t is in seconds. The propeller is originally at rest and the motor frame does not move.

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