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Houston…we have a problem http://www.youtube.com/watch?v=eco_xvkEQlg 1) You learned that if you push on a door far away from it’s hinges (the axis of rotation) it will be easier to open and close 2) You learned if you hang a mass farther away from your hand (the axis of rotation) it was harder to move up and down Don’t they contradict one another?

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So what exactly did we learn? The direction that you apply the force is rather important If you apply your force in the same direction as the object moves… less effort is needed with a longer lever If you apply your force opposite the direction that the object moves…more effort is needed with a longer lever

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What is torque? Torque is a tendency of a force to rotate an object about an axisforce A force applied to an extended object can produce a torque. This torque in turn causes the object to rotate.

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The object rotates about an axis. The lever arm is the distance (in meters) from the axis of rotation to the point where the force acts. The applied force is the force applied to the lever arm.

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Formula For Calculating Torque Torque = (force perpendicular to axis)(length of lever arm) τ = F l d τ = the Greek Letter Tau F l = Force perpendicular to lever arm d = length of lever arm.

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Calculating torque The torque (τ) the Greek Letter Tau, created by a force is equal to the lever arm (r) times the magnitude of the force (F).

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You try… A force of 50 newtons is applied to a wrench that is 30 centimeters long. Calculate the torque if the force is applied perpendicular to the wrench so the lever arm is 30 cm.

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You try… τ = r x F = 0.3 m x 50 N = 15 N-m of Torque Now lengthen the arm of the wrench to 0.7 m

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You try… If the doorknob was placed in the middle of a door, rather than at the edge..how much more force would be needed to produce the same torque for opening the door? Twice as much

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Balanced (Net) Torque The net torque is the sum of all the torques produced by all the forces Net-torque is zero or.. the torques are balanced Counterclockwise torque = clockwise torque

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Balanced (Net) Torque Equation F left x r left = F right x r right

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Calculate using equilibrium A boy and his cat sit on a seesaw. The cat has a mass of 4 kg and sits 2 m from the center of rotation. If the boy has a mass of 50 kg, where should he sit so that the see-saw will balance?

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A boy and his cat sit on a seesaw. The cat has a mass of 4 kg and sits 2 m from the center of rotation. If the boy has a mass of 50 kg, where should he sit so that the see-saw will balance?

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Less force is required farther out from the center of mass than closer in. So, by tackling a runner low -- far from the center of mass -- it takes less force to tackle him than if he were tackled high. Furthermore, if a runner is hit exactly at his center of mass, he will not rotate, but instead will be driven in the direction of the tackle. Similarly, coaches often advise linemen to stay low. This brings their center of mass closer to the ground, so an opposing player, no matter how low he goes, can only contact them near their center of mass. This makes it difficult for an opposing player to move them, as they will not rotate upon contact. This technique is critical for a defensive lineman in defending his own goal in the "red" zone, the last 10 yards before the goal line.

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Rotational Equilibrium and Rotational Dynamics

Rotational Equilibrium and Rotational Dynamics

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