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Chapter 8 Rotational Motion © 2014 Pearson Education, Inc.

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In a rotating object… The angle θ in radians is defined: where l is the arc length. © 2014 Pearson Education, Inc.

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For one full revolution… l = 2r = So… 2r r Then… = 2 rad

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Conversions 1 rev = 360 o = 2π rad

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A particular bird’s eye can just distinguish objects that subtend an angle no smaller than about 3x10 -4 rad. How small an object can the bird just distinguish when flying at a height of 100m? © 2014 Pearson Education, Inc.

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x = (theta) v = (omega) a = (alpha) © 2014 Pearson Education, Inc. New variables…

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Fill in the blank… A ____________ causes acceleration. A ____________ causes rotation. force torque

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Let’s pretend... You need to loosen a stuck bolt with a wrench... You aren’t strong enough...what do you do?

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When opening a door... Is it easier to open if you push close to or far away from the hinges?

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Torque Produces rotation = Fr Long arm, less force More force, shorter arm Ex. wrench, screwdriver, doorknob

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Because most things can rotate clockwise or counterclockwise we need + and – for direction. + is counterclockwise - is clockwise

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End of Chapter Problems 24, 25, 26, 29

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If…F = ma Then… = I I = moment of inertia

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Rotational Inertia Resistance to change in rotational motion Greater distance from center of mass to rotation point = greater inertia

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Why do baseball players “choke up” on the bat? “ Choking up” on a baseball bat will increase speed of swing

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Why do giraffes have a slower gait than Chihuahuas?

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Why do longer pendulums swing more slowly than shorter ones?

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8-5 Rotational Dynamics; Torque and Rotational Inertia I for various objects… © 2014 Pearson Education, Inc.

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End Day 2 © 2014 Pearson Education, Inc.

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If…F = ma Then… = I I = moment of inertia

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8-5 Rotational Dynamics; Torque and Rotational Inertia I for various objects… © 2014 Pearson Education, Inc.

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End of Chapter Problems 31, 37, 38, 40, 42

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Rotational Kinetic Energy ½ mv 2 Becomes ½ I 2

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Rotational Kinetic Energy K = translational + rotational K = ½ mv 2 + ½ I 2

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Problem Solving Strategy E = E U g = K t + K r mg y = 1/2mv 2 + 1/2I 2 Note – friction must be present No friction = no rolling (object will just slide)

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This will help… Linear velocity Radius = rotational velocity V = r

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End of chapter problems 50, 51, 52, 55

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End Day 3

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Angular Momentum If the net torque on an object is zero, the total angular momentum is conserved: Iω = Iω p = mv

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To change an object’s momentum… FΔt =Δp F = Δp/Δt = ΔL/Δt

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© 2014 Pearson Education, Inc.

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Rotational Dynamics 8.3. Newton’s Second Law of Rotation Net positive torque, counterclockwise acceleration. Net negative torque, clockwise acceleration.

Rotational Dynamics 8.3. Newton’s Second Law of Rotation Net positive torque, counterclockwise acceleration. Net negative torque, clockwise acceleration.

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