Solve Prob. 12-189 if the particle has an angular acceleration = 5 rad/s when =

Solve Prob. 12-189 if the particle has an angular acceleration θ̈ =  5 rad/s² when θ̇  = 4 rad/s at θ =  π/2 rad.

Prob. 12-189

A particle moves along an Archimedean spiral r = (80) ft, where is in radians. If θ̇ = 4 rad/s (constant), determine the radial and transverse components of the particle's velocity and acceleration at the instant = π/2 rad. Sketch the curve and show the components on the curve.

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r = (80) ft