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    Finding Angular and Relative Velocity

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    In solving use the coriolis accel concept and i j k vector coordinates.

    15.148 and 15.149 Pin P is attached to the wheel shown and slides in a slot cut in bar BD. The wheel rolls to the right without slipping with a constant angular velocity of 20 rad/s. Knowing that x = 480 mm when theta = 0, determine the angular velocity of the bar and the relative velocity of pin P with respect to the rod for the given data.

    15.148 a) theta = 0, b) theta = 90 degrees
    15.149 theta = 30 degrees

    © BrainMass Inc. brainmass.com February 24, 2021, 2:21 pm ad1c9bdddf
    https://brainmass.com/physics/relative-velocity/finding-angular-relative-velocity-15845

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    Solution Preview

    15.148)

    r = 140 mm
    R = 200 mm
    velocity of center of wheel (vc) = w*R = 20*200 = 4000 mm/s = 4 m/s

    a.)
    theta = 0 degree
    velocity of P (vp)= vc + w*r = 4 + 20*0.140 = 6.8 m/s
    AB = x = 480 mm = 0.48 m
    AP = 140 mm = 0.14 m
    Hence,
    BP = sqrt(0.48^2 + 0.14^2) = 0.5 m
    Let angle PBA = phi
    Hence, velocity omponent of P, perpendicular to BD:
    v_perp = vp*sin(phi) = 6.8*(AP/BP) = 6.8*0.14/0.5 = 1.904 m/s

    Hence, angular velocity of BD:
    wbd = v_perp/BP = 1.904/0.5 = 3.808 == 3.81 m/s --Answer

    velocity of P with respect to rod:
    v_parallel = 6.8*cos(phi) = ...

    Solution Summary

    This solution solves equations for velocity step-by-step to find the final velocity of points on the system.

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