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pg 73 - .3 Circular Motion car rounds a curve A satellite...

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Unformatted text preview: .3 Circular Motion ' car rounds a curve. A satellite circles Earth. A proton whirls around a giant particle ac— ' - lerator. Since they’re not going in straight lines, Newton tells us that a force acts on each "i g. 5.10). We know from Section 4.4 that the acceleration of an object moving with con- "-a It speed v in a circular path of radius r has magnitude vzlr and points toward the center _ the circle. Newton’s second law then tells us that the magnitude of the net force on an .z's-aject of mass m in circular motion is 2 Fm : ma : v (uniform circular motion) (5-1) r The force is in the same direction as the acceleration—toward the center of the circular path. For that reason it’s sometimes called the centripetal force, meaning center—seeking (from the Latin centrum, “center,” and petere, ”to seek”). J Centripetal force is not some new kind of force. It’s just the name for any forces that keep an obj ect in circular motion—which are always real, physical forces. Common ex- amples of forces involved in circular motion include the gravitational force on a satel- lite, friction between tires and road, magnetic forces, tension forces, normal forces, and combinations of these and other forces. Newton’s second law describes circular motion exactly as it does any other motion: by . relating net force, mass, and acceleration. Therefore we can analyze circular motion with the same strategy we’ve used in other Newton’s law problems. . Circular Motion-Whlrling ._a Ball on a String A ball of mass m whirls around In a horizontal circle at the .eiid of: 3' mass‘le'ss string of length. L (Fig. 5 1.13 The: string makes an angle 9 with the horizontal Find the hall’s. speed and the suing tension meme} This problefn" is similar to the Newton s law prohle'ms we worbd mvolVing force and acceleration The object of interest is the hall, and only two forces are acting on it: gravity and the string tension. aerator». Fights. 5.12 1.5 ciir. free body diagram- showing the two forces we’ We identified. The relevant equation is Newton’ 3 second law which becomes " ' - firi'z‘ing 5’ 5.3 Circular Motion 73 Elfillflfim A car rounds at turn on the Trans-Sahara highway. HEW Our {refit-Jody diagram for_ _ xthe whirling ball L - The hall’s _‘p.atli_ is In a hoiimntal plane; so its acceleration Is horizonml‘. _ , . _ _ Then two of the times- vectors in. our Iii-chi_e.rn.41"=1g and Iii-4am beam-— . : “4132;321:335an _ ' _' '. - ml or. vertical, sjo in developing our shonegy, we choose a horizontal] . . . . i _ vertical coorthnate System W A ball whirlihgl'on-a string, ' ' ' I Confli- ...
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