Meriam, Kraige & Bolton — Plane Kinetics of Rigid Bodies: Problem 6_162

6/162 A 55-kg dynamics instructor is demonstrating the principles of angular momentum to her class. She stands on a freely rotating platform with her body aligned with the vertical platform axis. With the platform not rotating, she holds a modified bicycle wheel so that its axis is vertical. She then turns the wheel axis to a horizontal orientation without changing the 600-mm distance from the centerline of her body to the wheel center, and her students observe a platform rotation rate of 30 rev/min. If the rim-weighted wheel has a mass of 10 kg and a centroidal radius of gyration \(\bar{k} = 300 \text{ mm}\), and is spinning at a fairly constant rate of 250 rev/min, estimate the mass moment of inertia \(I\) of the instructor (in the posture shown) about the vertical platform axis.