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'saject of mass m in circular motion is 2
Fm : ma : v (uniform circular motion) (51) 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 MotionWhlrling ._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
TransSahara highway. HEW Our {reﬁtJody 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 Iiichi_e.rn.41"=1g and Iii4am beam—
. : “4132;321:335an _ ' _' '.  ml or. vertical, sjo in developing our shonegy, we choose a horizontal] . . . . i _ vertical coorthnate System
W A ball whirlihgl'ona string, ' ' ' I Conﬂi ...
View
Full Document
 Spring '07
 KOPP
 Physics

Click to edit the document details