Serway & Jewett — Angular Momentum: Problem 34

You are advising a fellow student who wants to learn to perform multiple flips on the trampoline. You have him bounce vertically as high as he can, keeping his body perfectly straight and vertical. You determine that he can raise his center of mass by a distance of \(h = 6.00 \text{ m}\) above its level when he initiates the jump. He can do a single flip by bouncing gently, throwing his arms forward over his head, and tucking his body. You use your smartphone to make a video of him doing a single flip. Based on analysis of this video, you determine that his moment of inertia is \(I_{\text{straight}} = 26.7 \text{ kg} \cdot \text{m}^2\) when his body is straight and \(I_{\text{tuck}} = 5.62 \text{ kg} \cdot \text{m}^2\) in the tuck position. You suggest that he keep his body in the straight position for \(\Delta t' = 0.400 \text{ s}\) after leaving the trampoline surface and then immediately go into a tuck position. As he lands, he should straighten his body out \(\Delta t' = 0.400 \text{ s}\) before he lands. From analysis of the video recording, you determine that throwing his arms forward causes him to have an initial angular speed of \(\omega_i = 2.88 \text{ rad/s}\) as he leaves the trampoline surface. If he tries to bounce as high as he can, do some flips, and land back on the same spot on the trampoline, predict how many flips he can safely do such that he lands on his feet on the trampoline.