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Unformatted text preview: Dynamics 111: Motion in a Circle 7.1 Uniform Circular Motion 7.2 Velocity and Acceleration in Uniform Circular Motion 1. a. The crankshaft in your car rotates at 3000 rpm. What is the frequency in revolutions
per second? 3000 rev X in?“ : 50 15:!
[min 605 5 b. A record turntable rotates at 33.3 rpm. What is the period in seconds? 33.?2‘: x ‘62: g 05.55 red 2. The ﬁgure shows three points on a steadily rotating wheel.
a. Draw the velocity vectors at each of the three points. b. Rank in order, from largest to smallest, the angular velocities (01,
(02, and (03 of these points. Order: outage); Explanation: Eu)“ Psmﬁ ”traverses 'HM. SocNW. 0M5”.
"" ‘H‘t ”W' ‘tTWL . All pomh 0A the dual
reelwk ”Klk the Same ?£T'O& c. Rank in order, from largest to smallest, the speeds v1, v2, and V3 of these points.
Order:  V3 § 0, r. 0:. Explanation: UL“ \" w ‘ c9613 '5 is JPNHM”— cw! any ‘PTDM *Hu. . CMCis oR‘ he‘l‘a'ﬁoa QMQ So Mots 0k ﬁrmrec 3922:? ﬁlm» posit:
l anti 2! “Judx ourL rat ((kt Some. 1" gig each o'HnﬁJ“ 7_1 72 CHAPTER 7  Dynamics III: Motion in aCirclc 3. Below are two angular positionversus—time graphs. For each, draw the corresponding angular
velocityversustime graph directly below it. 9 A, a: a. a b.
ON: a
w
L_*———"‘.
0 . I u—__
3 . .
.' 4. Below are two angular velocityversustime graphs. For each, draw the corresponding angular
positionversus—time graph directly below it. Assume 60 = 0 rad. a. co b. ca 1 l Q:
Cb 5. A particle in circular motion rotates clockwise at 4 radr’s for 2 s, then counterclockwise at
2 radfs for 4 s. The time required to change direction is negligible. Graph the angular velocity
and the angular position, assuming 60 = 0 rad. 6. A particle rotates in a circle with or = 8 mfsz. What is a, if a. The radius is doubled without changing the angular velocity? : ”’1 3'
b. The radius is doubled without changing the particle’s speed? Misl— c. The angular velocity is doubled without changing the particle’s radius? M Dynamics III: Motion in aCircle  CHAPTER 7 73 7.3 Dynamics of Uniform Circular Motion 7. The ﬁgure shows a top view of a plastic tube that is fixed on a
horizontal table top. A marble is shot into the tube at A. Sketch
the marble’s trajectory after it leaves the tube at B. 'Tl‘" mwhla {pn'l'lvlmes in ax sﬁa'ﬁék l" (in: Top View of
horizontal tube one revolution, a very sharp knife is used to cut the
string at the instant when the ball is at its lowest point. Sketch the subsequent trajectory of the ball until it hits
the ground. Film ngc'l'oh is '{JNolbol‘s c. , lilac. ﬁne'1‘
oi“ at Horia—onl'allY lauackeaL produ‘hie. 8. A ball swings in a vertical circle on a string. During / 9. The ﬁgures are a bird’seye view of particles moving in horizontal circles on a table top. All
are moving at the same speed. Rank in order. from largest to smallest, the tensions T] to T4. v v
v m v 2m
®m gm Order: T3>Tl5Tﬁ7 ‘1
Explanation: '2.
r Smiler P. Case "l is He. same at: Case. l inseam \oo'l’la HA9. Mas: omﬂ
Hm magma. we— aﬂoatrude 74 CHAPTER 7 . Dynamics 111: Motion inaCircle 10. A ball on a string moves in a vertical circle. When the ball is at its lowest ‘\
point, is the tension in the string greater than, less than, or equal to the
ball’s weight? Explain. (You may want to include a freebody diagram as
part of your explanation.) R'l din lowes'l‘ poi‘4’, 'HI— aceelerd'han [r MParsr& . .5
Tina—s, 'HAQ +£ASI'OA magi" lat ﬁl‘ﬁa‘i‘r 'HAAIA ‘H'uL
wthbh‘l' $ar+lu and {ora. in lat use«Hui. 8L 1 1. A marble rolls around the inside of a cone. Draw a freebody diagram
of the marble when it is on the left side of the cone and a freebody
diagram of the marble when it is on the right side of the cone. ~—)
\ r“: {
w \ On left side On right side 12. A jet airplane is ﬂying on a level course at constant velocity. a. What is the net force on the plane? Fuel3 0
b. Draw a picture and identify all of the forces acting on the plane. FiH iiiHi : ml
F'Haruﬁ iF—HnrAsfl : \ F’“‘$l
(A “33 '63 c. Airplanes bank when they turn. Explain why, in terms of forces and physical laws.
Hint: What would a free—body diagram look like to an observer behind the plane? When HM. {pl4M» banks, in“, 'Mcludes as homes “hi Componed‘.
The. Moriwinl Componen'i' OJ" EH ?row‘m a. rqu'tauv vivaaural For“.
“teal2A +0 cams; “Hm. fleau. +0 Jrurn. Fromloehfral 'l‘LLPl,&n¢' Iu'l'kis Cast, ‘Ipltgpi > lwi ,W _:
'H'tt “liarm K: in OK “0““ “ﬁl —> F'W‘
dtruﬁOA 6* w Dynamics III: Motion in a Circle  CHA PTER 7 7'5 7.4 Circular Orbits 13. The earth has seasons because the axis of the earth’s M'Wbml PM" rotation is tilted 23° away from a line perpendicular \
to the plane of the earth’s orbit. You can see this in f      3:93
ad Find the ﬁgure, which shows the edge of the earth’s orbit
around the sun. For both positions of the earth, Nonhem winter Northem slimmer
draw a force vector to show the net force acting on 5°”th mm“ 8mm“ mm the earth or, if appropriate, write F = 0. 14. A small projectile is launched parallel to the ground at height h = 1 m with sufﬁcient speed to
orbit a completely smooth, airless planet. A bug rides in a small hole inside the projectile.
Is the bug weightless? Explain. Tim: gang is Wﬁlslfd—lﬁsx‘ Fm the range 'ikm‘ﬁ'l‘i's lvx 'Pv‘eeizaii
wi‘iirti‘n Proéec'itile , The leaf)" Sﬁtl bug‘s: weiak'i' 9'? U5: Muﬂﬂ. 7.5 Fictitious Forces and Apparent Weight 15. A stunt plane does a series of vertical looptheloops. At what point in the circle does the pilot
feel the heaviest? Explain. Include a freebody diagram with your explanation. ’TL‘L P'Ito‘k h‘XS iAtAUiQSQ' R‘i— 'HmL bO'H'DM cyp +L~¢L MCI.1 (Oi0‘9 . M
'HMST Po'm‘i' “at normal Rafa. on 'HNL PiiOT I5 aorta“ST, AS is TLn. +941: ’11". " h .
OtFrqren 5 Amy .F"“T “+09. E“
‘00 M' .5 4
w W Tilus din$756 063wa 4.4»). ?"\o't' a moving) «4' compﬂtalt. 8?},ch ‘ﬁxrowakﬂvdi 16. A rollercoaster car goes around the inside of a looptheloOp. Check the statement that is true
when the car is at the highest point and at the lowest point in the loop. Highest Lowest
The apparent weight wapp is always less than w
The apparent weight wapp is always equal to w
The apparent weight wapp is always greater than w — L
wan, could be less than, equal to, or greater than w L [At{kn intakes‘i' 93“, +1qu answerAcheaﬁs' mph ﬂagged oiHu Cal”. 76 CHAPTER 7  Dynamics 111: Motion in a Circle 17. You can swing a ball on a string in a vertical circle if you swing it fast enough. a. Draw two freebody diagrams of the ball at the top of the circle. On the left, show the ball
when it is going around the circle very fast. On the tight, show the ball as it goes around the
circle more slowly. J
3,1“
.e.‘ Us ”1' Very fast Slower b. As you continue slowing the swing, there comes a frequency at which the string goes slack
and the ball doesn’t make it to the top of the circle. What condition must be satisﬁed for the
ball to be able to complete the full circle? T? +1 WU}: : Muir . Tin. Minimum clown WN'D( fart—n. 'LS H" WLSMI
“1 r
'1. '1 __ , _._. i
’0 ma 1': mt.“ LJMIA 0(— “Min '— S/r— ”Jam" 9/!— 0. Suppose the ball has the smallest possible frequency that allows it to go all the way around
the circle. What is the tension in the string when the ball is at the highest point? Explain. :12: O . PH" H». SMaiiESf‘Fﬂme«cyf HAIL Ouhr (Aagiatliir
“A Mr‘ﬁ PDFGQ {5 +Lu. #Dr‘u 0‘? Elf“J“ﬁ ’ m ”grab“: 18. It’s been proposed that future space stations create “artiﬁcial gravity” by rotating around an
axis. (The space station would have to be much larger than the present space station for this to be feasible.)
a. How would this work? Explain. (Mir? T11; om'l'sloaa. wall 9'? HA1 Shﬁoq menial
frog/141.. ‘HM. 'i‘loot‘ Walk ‘Hru. ncr Mai “Fart; F('\V\:Mo( *1) We? Ha... OCCMPAA'h simianlead;
poi’3‘“) “NJ" ‘0; ‘i‘LLaHJAr'en'i “Rigidoi. 'HmL okjglc‘hr Tm «Nu mt‘ﬁﬁu‘d (adehf' b. Would the artiﬁcial gravity be equally effective throughout the space station? If not, where
in the space station would the residents want to live and work? Tia. appsamt MCBK+WLA beaku. iv an trimm9 normal kcLPmmM
bY Maud51M mu. As any; modes "mum—321m urn{lull thumb! . n. J 1
Micah9g baconAc manor Amt+0 kid—Smile!— NoQtMd. Y1: MUN) r. .n
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M . a ' ﬁver Dynamics III: Motion in aCircle  CHAPTER 7 77 7.6 Nonuniform Circular Motion 19. For each, ﬁgure determine the signs (+ or —~) of a) and a,. Speeding up Slowing down Slowing down Speeding up a1+ to" co+ (0' a, 4' a,_+_ a, "‘ a, _ 20. The ﬁgures below show the radial acceleration vector ('1', at four sequential points on the
trajectory of a particle moving in a counterclockwise circle. a. For each, draw the tangential acceleration vector 5, at points 2 and 3 or, if appropriate, write
a: = 0.
b. Determine whether a, is positive (+), negative (—), or zero (0). 2 21. A pendulum swings from its end point on the
left (point 1) to its end point on the right
(point 5). At each of the labeled points: a. Use a black pen or pencil to draw and label
the vectors 5i, and a, at each point. Make
sure the length indicates the relative size of
the vector. b. Use a red pen or pencil to draw and label off'0
the total acceleration vector 3 . 
O o o) 78 CHAPTER 7 . Dynamics III: Motion inaCircle ...
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 Fall '08
 Graff
 Physics

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