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Lecture series for Conceptual Physics 8th Ed. Rotational Inertia p118 Alias: momentum of inertia. The property of an object to resist being rotated T.R. Walker starts to fall. So, he pushes down on his right and pulls up on his left to right himself. The pole stays put. Whose legs have the least rotational inertia in fig. 7.3? Fig 7.5 Rotational inertias of some shapes: Why does disk beat hoop down ramp? Torque p121 Torque = lever arm x force fulcrum force mg At equilibrium: CCW torque = CW torque Torque = “la” x F =F x d Huh? Fl x dl = Fr x dr 300 x dl=500 x 1.5 dl=2.5m Center of Mass and Center of Gravity p123 Fig 7.11 shows the ball following a smooth parabola and the bat wobbling. In both cases, the CM makes a smooth parabola. The white dot marks the CM of the adjustable wrench. The CM goes straight! Center of Gravity is basically the same as CM. Locating the Center of Gravity p 124 Tccw = Tcw NOTE: The weight of the stick acts at its center of gravity. For weird shapes: For athletes: Which one is more stable? Stability p125 Equilibrium exist when your CG is over your support. Whoops! The amount of stability is determined by how high the CG must be raised in order to tip the object over. Most stable U=mgh? More Stability In fig. 7.24 which has the greater torque around the imaginary fulcrum? This one? No This one? Yes What contributes to its greater torque? Longer lever arm Peter Parker fooling around. More mass (force). Centripetal Force p128 The force on a moving object that is directed towards a fixed center. Is the water forced away from the clothes? No! The clothes are forced away from the water. 5g – 1g Loose mud flies off on a tangent. 5g + 1g Centrifugal (the imaginary) force p129 When the car stops and you’re “thrown” against the dashboard, you don’t say a force pushed you forward. You say, “My inertia kept me going and the dashboard pushed on me.” The bug wants to go in a straight line but the can pushes it toward the center Does the bug say, “I’m pushing on the floor?” Centrifugal Force in a Rotating Frame p130 The silly bug still thinks that it is in a stationary can pushing on the floor. You are lighter at the equator. Bugs in the space tire think that they have “gravity”. ? Simulated Gravity p 131 A force toward the center. The action force The reaction force But, this is an imaginary force. If the floor were to give way, would he fly away from the center? NO! He would sail off on the tangent. Angular Momentum p133 You remember, of course, that linear momentum, p, = m x v. Since mass and inertia are aspects of the same thing, then you wouldn’t be surprised that… AnguLar momentum = rotational inertia x rotational velocity Given: =v / r L=I (I = mr2 or I = ½ mr2, etc.) So, L = mr2 v r = mvr What is angular momentum of the ball if m = 2kg, v = 3m/s and r = 4m? L=mvr=(2)(3)(4)= 24kg-m2/s Conservation of Angular Momentum I = I A gymnast balls up to increase his spin rate. A falling cat rotates its front half to rotate the back in the other direction, then straightens out for a 4 footed landing The end p134