Lab 5 key - PHS 381 Biodynamics /MOVEMENT ANALYSIS Learning...

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PHS 381 - Biodynamics CONSERVATION OF ANGULAR MOMENTUM /MOVEMENT ANALYSIS Learning objective (angular momentum): To increase understanding of angular momentum. This includes understanding how increase/decrease angular momentum and understanding when angular momentum is conserved. Additionally, to understand and explain differences between linear and angular momentum. For full credit on the questions include complete explanations and the formula(s) that support your answer. Equipment: swivel chair Equations you may need: I = mk 2 H f = I i ϖ i = I f ϖ f = H f T = I α Tt = H H total = H arms + H legs + H torso ANGULAR MOMENTUM Review Newton’s First Law of Motion as applied to angular motion (Conservation of Angular Momentum) The angular momentum of an object is conserved (it stays constant) if no external torques act on the object. Demonstrate by throwing a pen up in the air and spinning it. Ask what happens. Does the pen change its rate of spin while it is in the air? Does it spin faster or slower? The pen spins at a constant rate - because there are no external torques acting on it while it is a projectile. What about the force of gravity - doesn’t it create a torque on the pen? No - since this force acts through the center of gravity and the axis of rotation is also through the center of gravity - so the moment arm of the force of gravity is zero. Gravity, therefore, causes translation but not rotation. Newton’s First Law applied to angular motion can be expressed as: H i = I i ω i = I f ω f = H f = constant initial angular momentum = final angular momentum = constant if no external torques act Angular momentum of body can be approximated as the sum of the angular moment of the parts. Chapters : Chapter 7 (angular kinetics), Chapter 4 (work, power, energy)
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PHS 381 - Biodynamics Name ________________________________________ Activity 1: Spin in chair with legs extended and arms extended and weights in hands (weights are optional but increase the effect we are examining), then pull arms and legs in towards chair. What happens when we are spinning and we pull our arms in.? Why? (5 pts) When I pulled my arms in closer to my body, I began rotating faster. When my arms were out, my moment of inertia is higher than it is when my arms were pulled in. Since angular momentum is conserved, when I pulled my arms in, the moment of inertia decreased, which thus caused the angular velocity to increase, because the momentum must be conserved. (The formula for this is H a = I a w a ) So, when one of either inertia or angular velocity increases, the other must decrease in order for momentum to be conserved. Angular momentum is conserved, because in a closed system, angular momentum remains constant. Can we change our angular momentum while we are spinning in the chair without pushing off on something? Why or why not? (assume the absence of friction and wind resistance) (5pts) No. if there is no friction angular momentum is conserved: It’s a closed system. It may seem like we can, because we can pull our arms in, and then push our arms out, and pull them back
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