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I PHYSICS 116 CYCLEZ » a _‘ d; ’
INDIVIDUAL SUMMARY PROBLEMS: ROTATIONAL KIN .MA TICSJ “s. . .~;. angular velocity u) and the angular acceleration a. i , . . . .
Use the notation (8) = into the page, ° =_ out of the page, and 0 = zero magnitude. ; 1. The disk below is free to rotate about a vertical axisthrough its center. Indicate the direction of the p F
l The disk is rotating. For a point'A on the edge; v(0) = 5 m/s; v(10) = 2 . ‘ ‘. “:58 H
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, Direction of rotation , " . ' V ‘ w if h I
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/ . w = M o D ‘ 3471;“ I
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V ., .. l m : @ ® ' A .51. ‘8 2. A 900 kg car (including the tires) accelerates uniformly from rest and reac s a speed of 20 m/s in 10
sec. The diameter and mass of each tire is 58 cm and 5 kg, respectively. S f l i l ._ ‘ 11 . 201V] (9 _ l (a) F i'nd the ﬁnal rotational speed ofthe tire in revolutions per second. (A) = 1‘ ; ﬂ 57 r l {Z 1: mm 2;“. (b) Determine the total kinetic energy of the car after, it has reached its ﬁnal speed of 20 m/s. PHYSICS 116 CYCLE 2
GROUP S UMMAR Y PROBLEMS: ROT A T IONAL KINEMATICS
(EEORKSHOP M4KEUP+SUMMARZ2  “wan, I. Pre arato Skills~ "
1 Converting Between Revolutions & Radians
The angular displacement A0 corresponding to I revolution =2 Jr radians Do the following conversion exercises : i J“
1. 1/2 rev = Tr“ rad 2. 2 rad = TC rev 3. 3 rev = “\T rad 4. 5n rad = Z . 5—. rev s ‘/B. Relating Linear and Rotational (Angular) Values Another important skill in analyzing rotational motion is being able to relate the quantities of rotational
motion about a ﬁxed axis (0,m,or a) to those of one dimensional linear motion (x, v, or a). When doing
this, be sure that the rotational quantities are measured in radians, and that the radius of rotation, R, is in
meters. Then use the following relationships where appropriate: (1) x = GR (in meters) and 0 = x/R (in radians)
(2) v = 00R (in m/sec) and o) = v/R (in radians/sec)
(3) a = OR (in m/sz) and a = a/R (in rad/52) . Complete the following sentences. Draw a picture for each exercise. 1. A point rotates through 27: rad at a radius of 0.6 meter. The distance traveled, x, by the point is
, a Z m.
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2. A point rotates at a rate of 4 rad/sec at a radius of 0.25 meters. The linear speed, v, of this point
is [ m/sec. _ L(
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3. A point on a sphere of radius 0.3 meters is o ting wit? a linear acceleration of 0.66 m/secz. The
an ar acceleration, a, of this oint is M rad/s .
gul p D< 5 a: =~ a 2 o 2‘; at e,“ """"
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4. A wheel of radius 0.75 meters rotates through a distance of 22 meters. The number of revolutions through which the wheel turned is fig (‘2 2 rev. .Z/Q’ﬁQD/é ‘3 ’ °757n XCZZM
a; Zn” S. The disks below are ﬂee to rotate about a vertical axis through their centers. For each situation, a
indicate the direction of the angular velocity u) and the angular acceleration a. Use the notation (8) = into the page, ' = out of the page, and 0 = zero magnitude. 7 *' *1 (a) The disk is rotating. For a point A on the edge : v(0) a P nus; v(10) = 3 m/s. ¢ Direction of rotation (this arrow does NOT represent (1)) (b) The disk is rotating. For a point A on the edge; v(0) = 3 m/s; v(10) = 1 m/s. Direction of rotation N f g .
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7 dcijd/Zzoimm’ﬁmzm ' m: .5 atics. For part (c) use energy considerations]. P X a Find the number 03 revolutions the‘ wheels m bib) Find the ﬁnal rotational spbed of the tire in r II. Problem Solving this motion, assuming no slip ing. ao= \/ zz.= 22/.201 =75: 559 er “Zlfdlﬁ olutions per second. ind the amount of work done in accelerating the car. (J = Fol a €cvwx7OQ =M0\OL = 8CD~2.S’~017.Z 2. A hoop (Ihmp=MR2) and a disk roll (REEL/1M1?) down a plane that is 1 m high.
' 8’ ind the ratio of rotational kinetic energy to translational kinetic energy for each object. \ L b) Which one wins? Explain. 5i$i< % W OF MASS WH$ Ci" To *’
_ _ % $12341 T—'—> leH \9
t @ Fmd the speed of each object at e bottom of the lull. °
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This note was uploaded on 02/06/2012 for the course PHYSICS 115 taught by Professor Brahmia during the Fall '08 term at Rutgers.
 Fall '08
 Brahmia
 Physics

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