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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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8.4. Newton’s Second Law for Rotational Motion

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