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Unformatted text preview: PH 131 FALL 2000 HOMEWORK # l3 Assigned: 11/27/00
Due: 12/06/00 (( SE. A 140 kg hoop rolls along a horizontal ﬂoor so that its center
of mass has a speed of 0.150 mls. How much work must be dune
on the hoop to step it? ssm 3?. A constant horizontal force of magnitude [0 N is applied to a
wheel of mass [0 kg and radius 0.30 m as shown in Fig. 1230.
The wheel rolls smoothly on the horizontal surface, and the accel
eration of its center of mass has magnitude 0.60 misz. (a) What are
the magnitude and direction of the frictional force on the wheel? (b) What is the rotational inertia of the wheel about the rotation
axis titrough its center of mass? 28 :max
+1? 241460;”, CHIZ— 25E 25E. Two objects are moving as
shown in Fig. 1235. What is
Lheir total angular momentum 6.51:3 about point 0'? ilw ”'2 $39—92? m/s 2 V2. .5 m \7.
L? é? @ixﬁ Q4 2 @1190“
r .3
~32 @3sz
£2 '
£2 2 maﬁa;
1.2 mm)! : ww: WWI :: E (3. 0 (5696142)
.— (6.90.5)0291 k3 MML/is : 51.9; 2.4123725 \ . cot/7: 355 55E, Three particles. each of mass m, are fastened to each other and to a rotation axis at 0 by three
massless strings. each with length
d as shown in Fig. 126?. The
combination rotates around the
rotational axis with angular ve
locity w in such a way that the
panicies remain in a straight line.
In terms of m. d. and w. and rel ative to point 0, what are (a) the rotational inertia of the combi
nation, (b) the angular momentum of the middle particle. and
(c) the total angular momentum of the three particles? 55m GEMIN R: 0.50 rm rm = '0 “3
T; Peﬂbd 9% “rotalb. =25 5 FIND” (_ao = 5+ruclurc's foreliml
I” “mewHat. and) 0’) «L: Am ulm" mmMu/m
éme{vqrz . 53?. Figure 1239 shows a rigid structure consisting of a circular
hoop of radius R and mass m, and
a square made of four thin bars,
each of length R and mass m. The
rigid structure rotates at a con—
stant speed about a vertical axis.
with _a period of rotation of 2.5 s. ASSuming R = 0.50 m and m =
2.0 kg. calculate (a) the struc
ture‘s rotational inertia about the
axis of rotation and (13) its angular
momentum about that axis. ' Ca) use. ea. Ltz‘ttncpgmiml axis Aneofm] from book '
Icw = W more 92 Circular hoe? atmt «ws 54M
: MEL l —_'2 qn’RZ (us‘ima (tabla 01C P3 . 7.461 in book)
:2 % mR'Iu 0 ~ I
: raaw we. bar)+ 1: (Late Vet{um}. bar) \\ Z
+ QXIC horizomlaov 54““) mm #093?“ square ll )3
13
75‘
~52)
“'3‘
1.3,
6; D
{J
h
E 1.
r w "G W mm
2—65 " (£1412.  3‘? E 39E. A man stands on a platform that is rotating (widtout friction}
with an angular speed of 1.2 rew‘s; his arms are outstretched and
he holds a brick in each hand. The rotational inertia of the system
consisting of the man. bricks. and platform about the central axis
is 6.0 kg  m3. If by moving the bricks the man decreases the re
tational inertia of the system to 2.0 kg  m3, (at) what is the resulting
angular speed of the platform and (b) what is the ratio of the new
kinetic energy of the system to the original kinetic energy? (c) What
provided the added kinetic energy? 85m $1 GuamT: 6% .iL’m
Jig—J M ‘l‘k‘l’hl'l‘l‘ﬂ; Lita. aw; . tat/“i
L: (OI McMME» Co‘s—meal.  ‘2) Mill KE 50 SHEETS
IOO SHEETS 22144 200 SHEETS 2244]
22142 @ 48?. A girl of mass M stands on the rim of a frictionless merry—gr» '
round of radius R and rotational inertia I that is not moving. She
throws a rock of mass m horizontally in a direction that is tangent
to the outer edge of the merryg0~r0und. The Speed of the rock.
relative to the ground, is v. Afterward. what are in) the angular
speed of the menygomund and (b) the linear speed of the girl? [a TD? VJELO THE JRL’ lLJMéI'IKZ SPEED 1:9 eat/EM B‘r‘i LONSJMK. g—Axts To BE ALchcjy _
Kw A710” AXE" (P05. 019'?" 0F PAéE'b W‘— 22]4] we... 22142 50 SHEETS
100 SHEETS 221 44 200 SHEETS 37V 57P. In Fig. 12415. a 1.0 g bullet is ﬁred into a 0.50 kg block that
is mounted on the end of a 0.60 m nonuniform rod of mass
0.50 kg. The block—rod—bullet system then rotates about a ﬁxed axis at point A. The rotational in ertia of the rod alone about A is 0.060 kg  m3. Assume the block is small enough to treat as a par ticle on the end of the rod. [3) What is the rotational inertia of the block—rodwbullet system about point A? (b) If the angutar speed of the system about A just Q—u
after the builet’s impact is 4.5 Bullet radfs, what is the speed of the bul 59‘ 1245 Problem 51
let just before the impact? i 15997:?“ " ‘LP—Db + LBLaCK— rl‘BvLJ—ET
h .__ 2 2.
2': Lite!) '9' M r‘ + MBUH—L’T {— E COMégm/NTJOM 07“ ANGOLAR MOMEMTUM'. _. __.. aomstbaz zAxts. To 35 f
1—; = Z. Alf0&6 ?077 Axis CPDQ. 96)" OF PAéQ)
3
L}? ‘: Lfﬁ E
i
 O _ '—' i i
mbuuETVI; FW?O " ‘stsrgm “31° g
V ... Lﬁféﬂzm “DJ: E
I ‘ M0755
 ' L  1M 0‘ TI?)
: BuuaT " FwdET ' = ts. n—...._..__—m~__—— ...
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 Fall '10
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 Physics, Work

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