A gymnast jumying onto a bar can swing herself around it at high speed. Assume she is 160 cm tall, and that she has the moment of inertia of a thin rod. A. The center of gravity of her torso (with mass 35 kg) is a distance of 50 Cm 'om the top of her head, and the center of gravity for her legs (with mass 23 kg) is at a distance of 110 cm from the top of her head. How far is her center of gravity from the top of her head? B. If she jumps onto a gymnastics bar with her body at an angle of 25 below the horizontal, as shown above, draw an extended free body diagram clearly indicating the pivot (i.e. the axis of rotation). C. What is the net torque on the gymnast about the pivot you indicated? Her head is 49 cm from the bar. D. Using the result of C, find her angular acceleration (for the moment of inertia, you may model her as a thin rod rotating about its end). E. How do the following quantities change, as she begins rotating around the bar? Explain your reasoning for each case. 1. The net torque on her body. 2. Her angular acceleration. 3. Her angular velocity. F. If the maximum linear velocity her center of mass reaches is 2.3 m/s, what is her maximum angular velocity? G. Use the answer to part F to find the maximum linear velocity experienced by her feet.H. If the mass of each foot is 0.9 kg, what is the maximum force that each ankle exerts on her foot? Hint: Draw :3 FEB. When we hold a weight at arm's length at the height of our shoulder, the deltoid muscle is larger responsible for keeping our arm and the object at their xed height. To estimate the tension in the Deltoid, we model the arm as in the drawing below, with all forces acting on the arm at the indicated distances from the origin (0). The arm's mass is 10 kg and its weight g\" acts on the center of gravity (CG), while the small obj ect's mass is 6 kg, and it exerts a force led all the wa).r at the end of the arm. The deltoid exerts a force at an angle of 9 = 15. I FEWIA l N P 3 6 cm For all questions below, torques are measured relative to the origin {0) and counterclockwise rotations are positive. A. What is the torque (in N - In} exerted by FE\"? \fC. For the arm+object system to be static, what is the torque exerted by the deltoid muscle? Express your answer in N ' m. D. If the system is in equilibrium, what is the magnitude of the tension, |Fr], in Newtons? E. If you look carefully at the above diagrams, the system cannot truly be in static equilibrium because the sum of the drawn forces is not zero. There must be a force on the arm acting at the origin (O) exerted by the scapula. What are the x- and y- components of this force? F. Your answer to question D. should be a rather large number, compared to the other forces given in the problem. If we could design the deltoid so as to minimize the force it needs to provide to keep the system in equilibrium, what angle 0 would minimize the tension on the deltoid muscle? (Assume only the direction of Fr changes; all other forces remain the same.)