Motion System Design

Fun with Fundamentals Puzzler: Free for ball

See the previous problem: This ship is a-sailing.

Every November, fans gather for the Otheta State vs. Cactus U match-up. This year, it's late in the first quarter — third and ten — and OSU's Johnny T. Jectrie fades back to pass. He lays out a tight spiral, but a Cactus rascal deflects the ball at the line of scrimmage — imparting an end-over-end tumble to the ball's motion.

If the ball's spin is directed as shown as it tumbles towards one very tightly covered receiver, and it's gyrating at Ψ = 4 rad/sec, what is its angular velocity?

Assume that the ball's ratio of axial to transverse moments of inertia is one third, measured with respect to the center of mass.

Show me the solution.

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