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Particle vs. Rigid-Body Mechanics

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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Particle vs. Rigid-Body Mechanics

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  1. 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 motionof any single particle (pt)in body particle Rigid-body (continuum of particles)

  2. 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 B B B A A A A

  3. Kinematics of Translation y • Kinematics • Position • Velocity • Acceleration • True for all points in R.B. (follows particle kinematics) rB rA x B A

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

  5.  r Rotation about a Fixed Axis– Angular Motion • Point P travels in circular path (whether “disk” or not) • Angular motion • Angular position, θ • Angular displacement, dθ • Angular velocity ω=dθ/dt • Angular Acceleration • α=dω/dt • Angular motion Equations 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 )

  6.  r v v ∆v an an ∆v a a at an Rotation about a Fixed Axis – Motion of Point • Point P travels in circular path • Position of P • Defined by r • If body rotates some dθ, then displacement is ds = r dθ • Velocity (tangent to path) • Acceleration (2 components)

  7. 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/s2, 8.38 s)

  8. Example Problem The gear A on the drive shaft of the outboard motor has a radius of rA = 0.5 in and the meshed pinion gear B on the propeller shaft has a radius rB = 1.2 in. Determine the angular velocity of the popular in t = 1.5 s, if the drive shaft rotates with an angular acceleration a = (400t3) rad/s2 , where t is in seconds. The propeller is originally at rest and the motor frame does not move.

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