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Torque Not just a crappy movie with Ice Cube http://www.impawards.com/2004/posters/torque.jpg

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What Torque is Torque is a force that produces a rotation Think about using a wrench to turn a bolt Torque depends on TWO THINGS: – How much force you apply – How far away from the center of rotation you apply it http://upload.wikimedia.org/wikipedia/commons/2/21/Torque.JPG If F A and F B are equal, which will produce a greater torque in this example?

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Torque The distance from the center of rotation to the location the force is applied is called the LEVER ARM. In general, we care about the part of the force that is applied PERPENDICULAR to the lever arm F1F1 F2F2 F3F3 Let’s say that the lever arm rotates around a pivot point to the left. If all three forces are the same magnitude, which one produces the greatest torque? Pivot Lever arm

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Torque: strange units Torque is kind of like force, ‘cept different. Force is a part of torque, but it also depends on that lever arm. So torque is equal to force X length of the lever arm Force is in Newtons, Length is in meters So torque is given in Newton-Meters (or in foot-pounds if you are in the English system).

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Perpendicular Force It’s just like when we were talking about vectors A force at an angle will have a component that is perpendicular to the lever arm. What components of the forces below are perpendicular to the lever arms?

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Torque brainstorm Give some examples of torque that you use on a daily basis

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Balanced Torques Torques are forces (basically) and they can be in equilibrium with one another. Example: kids on a teeter-totter (or seesaw or whatever the youth of today call these devices). – Weight provides force, seesaw is lever arm Let’s say you and a friend are on either end of a seesaw. If you weigh the same amount, then how far should each of you sit from the pivot? Now assume the unlikely scenario that the two of you are different weights. Where should you sit?

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Torque example: IGNORE CRAZY UNITS http://microship.com/resources/resourcepix/cgdb-1.jpg

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Rotational Inertia – Yes, it’s what you think Remember inertia? Yeah, that was awesome. Inertia was the tendency of an object in motion to stay in motion. Likewise, rotational inertia is the tendency of an object that is rotating to keep rotating. Just like it takes a force to change the linear state of motion, it takes a torque to change the rotational state of motion.

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A subtle but important difference For linear motion, inertia depends on mass But rotational inertia depends not only on mass, but also on its DISTRIBUTION. The closer in the mass is to the center of rotation… – The less rotational inertia – The easier it is to get rotating – The easier it is to stop rotating once it starts The farther the mass is from the center of rotation… – The greater rotational inertia – The harder it is to get rotating – The harder it is to stop rotating once it starts

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Examples and Demonstrations “Choking up” on a baseball bat Short Pendulum Vs. Long Pendulum Animals (including you) running Weights on a bar Flipping pencil between fingers Rolling hoops and disks Gymnastics and other spinning people

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Angular Momentum Rotational inertia of an object X how fast it’s rotating Angular momentum can be conserved If you change the rotational inertia, the rotational speed will also change to compensate Examples – Guy in chair with weights – Flywheels – Gymnasts

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Rotational Mechanics Rotational Motion Rotational Speed or Angular Speed Typically measured in rpm’s or degrees/sec, but the SI unit is radians/sec ω.

Rotational Mechanics Rotational Motion Rotational Speed or Angular Speed Typically measured in rpm’s or degrees/sec, but the SI unit is radians/sec ω.

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