Chapter 12.1, Problem 12.68P

The 3-kg collar B slides on the frictionless arm AA'. The arm is attached to drum D and rotates about O in a horizontal plane at the rate $\stackrel{\text{'}}{\theta }=0.75$ t, where $\stackrel{\text{'}}{\theta }$ and t are expressed in rad/s and seconds, respectively. As the arm-drum assembly rotates, a mechanism within the drum releases cord so that the collar moves outward from O with a constant speed of 0.5 m/s Knowing that at $t=0,r=0$ , determine the time at which the tension in the cord is equal to the magnitude of the horizontal force exerted on B by arm AA'.