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Ch 11 Rolling, Torque, Angular Momentum - 11 CHAPTER R O L...

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Ch 11 Rolling, Torque, Angular Momentum

Ch 11 Rolling, Torque, Angular Momentum - 11 CHAPTER R O L...

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WHAT IS PHYSICS? As we discussed in Chapter 10, physics includes the study of rotation. Arguably, the most important application of that physics is in the rolling motion of wheels and wheel-like objects.This applied physics has long been used. For ex- ample, when the prehistoric people of Easter Island moved their gigantic stone statues from the quarry and across the island, they dragged them over logs acting as rollers. Much later, when settlers moved westward across America in the 1800s, they rolled their possessions ±rst by wagon and then later by train. Today, like it or not, the world is ±lled with cars, trucks, motorcycles, bicycles, and other rolling vehicles. The physics and engineering of rolling have been around for so long that you might think no fresh ideas remain to be developed. However, skateboards and in- line skates were invented and engineered fairly recently, to become huge ±nan- cial successes. Street luge is now catching on, and the self-righting Segway (Fig. 11-1) may change the way people move around in large cities. Applying the physics of rolling can still lead to surprises and rewards. Our starting point in exploring that physics is to simplify rolling motion. 11-2 Rolling as Translation and Rotation Combined Here we consider only objects that roll smoothly along a surface; that is, the objects roll without slipping or bouncing on the surface. Figure 11-2 shows how complicated smooth rolling motion can be:Although the center of the object moves in a straight line parallel to the surface, a point on the rim certainly does not. However, we can study this motion by treating it as a combination of translation of the center of mass and rotation of the rest of the object around that center. 275 ROLLING, TORQUE, AND ANGULAR MOMENTUM 11 CHAPTER 11-1 275 Fig. 11-1 The self-righting Segway Human Transporter. (Justin Sullivan/Getty Images News and Sport Services) Fig. 11-2 A time-exposure photograph of a rolling disk. Small lights have been at- tached to the disk, one at its center and one at its edge.The latter traces out a curve called a cycloid. (Richard Megna/Fundamental Photographs)
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276 CHAPTER 11 ROLLING, TORQUE, AND ANGULAR MOMENTUM To see how we do this, pretend you are standing on a sidewalk watching the bicycle wheel of Fig. 11-3 as it rolls along a street.As shown, you see the center of mass O of the wheel move forward at constant speed v com . The point P on the street where the wheel makes contact with the street surface also moves forward at speed v com , so that P always remains directly below O . During a time interval t , you see both O and P move forward by a distance s .The bicycle rider sees the wheel rotate through an angle u about the center of the wheel, with the point of the wheel that was touching the street at the beginning of t moving through arc length s .Equation 10-17 relates the arc length s to the rotation angle u : s ± u R , (11-1) where R is the radius of the wheel. The linear speed v com of the center of the wheel (the center of mass of this uniform wheel) is ds / dt . The angular speed v of
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