Consider a slender rod AB of mass m and length L pinned at its midpoint O to a vertical shaft. The rod can rotate by θ about the pin, and the shaft can rotate by φ about its long axis. The mass of the shaft and collar may be neglected. The cord keeps the rod at an initial angle of 30? with the vertical while the shaft is initially rotating freely at angular velocity φ? = 200 rad/s. The cord suddenly breaks.
a. Find an expression for the tension in the cord before it breaks.
b. Find the differential equations of motion for the rod (θ¨ and φ¨) after the break.