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Transcript
Zero Torque and Static Equilibrium If the net torque is zero, it doesn’t matter which axis we consider rotation to be around; we are free to choose the one that makes our calculations easiest. 1 How do we incorporate the plank into the problem? Recall when an object has a symmetric shape and its mass is uniformly distributed, the center of mass is located at the geometric center. The center of mass for any extended object provides the distance from the axis of rotation of the resultant torque from gravitation forces acting on every point on that object. L/2 mp g Total force acting on the plank =0 Total torque acting on the plank =0 Torque equation involves only 1 unknown force F2 Solve for F2 Substitute F2 into the force equation and solve for F1 2 What is the maximum distance x from a smooth frictionless wall you can put a 100N uniform ladder of length 5.0m on a floor where the coefficient of static friction is 0.40? The equilibrium condition the force exerted by the wall is equal to the force of friction the normal force Fn determines the maximum force of static friction x Choose ground‐ladder interface as pivot point, but you could choose any point and the result would remain the same. The sum of the torques must equal zero because we are in equilibrium. Substitute for 3 Rotational Kinetic Energy and the Moment of Inertia The total kinetic energy of a rolling object is the sum of its linear and rotational kinetic energies: The second equation makes it clear that the kinetic energy of a rolling object is a multiple of the kinetic energy of translation. An object starts at rest at the top of an incline plane and rolls without slipping to the bottom What is the object’s speed on reaching the bottom? v Equating initial and final energy we have the relationship Solving for v Conservation of Energy If these two objects, of the same mass and radius, are released simultaneously, the disk will reach the bottom first – more of its gravitational potential energy becomes translational kinetic energy, and less rotational. Vi =0 Water and Ice Bottle Race vf Independent of R and M vf I = 0 for water bottle I = ½ MR2 ice bottle 7 A block with mass m1 of 2.4kg is connected to 2nd block of m2=1.8 kg by a rope wrapped around a pulley of mass m3=3kg and radius of R=15cm. If d=20cm, what is the speed of m2 just before hitting the ground? 8 9 rolling sphere A, vA=0 D, vD h B, vB R 2R y y x C, vc=max velocity y=0, U=0 Point B: let y be a variable for every point Point D: (1) However there is an addition condition for point D for the ball to stay on the track (2) (1) Substitute equation (2) for vD Min criteria Solve for h Clicker What is your quest? A) B) C) D) Who would cross the Bridge of Death must answer me these questions three, ere the other side he see. find the Holy Grail learn more physics and control the world locate the perfect Shrubbery Burn Witches