# Chapter 8 Rotational Motion © 2014 Pearson Education, Inc.

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Chapter 8 Rotational Motion © 2014 Pearson Education, Inc.

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

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

Conversions  1 rev = 360 o = 2π rad

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.

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

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

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

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

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

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

End of Chapter Problems 24, 25, 26, 29

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

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

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

Why do giraffes have a slower gait than Chihuahuas?

Why do longer pendulums swing more slowly than shorter ones?

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

End Day 2 © 2014 Pearson Education, Inc.

 If…F = ma  Then…  = I   I = moment of inertia

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

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

Rotational Kinetic Energy ½ mv 2 Becomes ½ I  2

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

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)

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

End of chapter problems  50, 51, 52, 55

 End Day 3

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

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