Chapter 8 Rotational Motion and Equilibrium
1. Give explanation of torque in own words after doing balance-the-torqueslab
I
as an inquiry introduction
1. The distance between a turning axis and the point of contact of a perpendicular force is called the fulcrum.
a. T
b. F
False: it is the moment arm
2. To turn a stubborn screw, it is best to use a screwdriver that has a
a. long handle
b. wide handle
c. yellow handle
d. red handle
B Wide handle is greater torque
/
e.none
B - see text
r-
8. A ball resting on the floor is in what kind of equilibrium?
a. Neutral
S
b. Stable
c. Unstable
'YZ. stable.
3.
[ft~If! ()It N [f
(). TILl}
L,
See the book p 213.
Determine whether an object will tip over based on locations of axis of rotation
and center of mass
10. An unaided object will topple over when its center of gravity extends beyond its support base.
a. T
rl\(Jl:tl5I7Cf(
b. F
True: see lab and book
I
'---4 ~
.
11. When you carry a heavy load with one arm like a bucket full of water, why do you tend to hold your free
arm awa from your body?
to chan e the center
0
\
gravity of your body and the load
b. to change the mass of your 0 y
c. to look way sweet
d. to change how much weight you and your load has
A- see lab
12. If an object is in stable equilibrium,
any displacement will
"
a. decrease its mass.
b. lower"
of
ravity.
c. raise its center of gravity.
ase its mass.
e. neither raise nor lower its center of gravity.
c -See book.
4.
c.U.V
~
r
IJ~ ",foQ.D.
(.A-~.
Calculate torgue. include situations where force is not perpendicular
to radius
15. You exert 300 Newtons of force on your bike pedal at an angle of 60 degrees. The length from the axis of
rotation on the wheel to the pedal is 20 centimeters. What torque do you apply to the bike wheel?
a. 51.96 N.m
b. 60 N.m
c. 5196.2 N.m
d. 6000 N.m
A~
fx r :::;
f Y (,.lAQ- - (p, Z-0'0(366
tJ'f£iA
toj
5.
Calculate
missing torque
needed
17. Two people sit on a balanced
person's
to establish
see-totter.
end of the see-totter
equilibrium
When one person leans toward
the center of the teeter-saw,
that
will
a. fall
b. rise
c. stay at the same level
B - moment
arm decreases
18. A 400-gram mass is attached to the 20-cm position on a meter stick that is suspended from a hanging
string at the 50-cm position. If a mass of GOO-grams is attached to the second side of the suspended stick, at
what METER STICK POSITION should you attach the GOO-gram mass?
I
I
tk,
~
\-:s
a. 90 cm
I
f~
;l'=- {)f- aK,~J-ro,...f,.•.••
0 ~{>,3,,,.:)(-....~?~)(\)t [(ISSUf-J:LI~
Lf{j)~" O,ttay
f,~Q,~061~lwfl0
117bN"'~
3\~l~
fL($-.Zi5N)
.
Fl ~~,tO(~)~~/fi~
C-Usetorques.
~
f..'L" 0 ~ (r:,,;J t~2Xf •..>~f~)
0 :-(.t, ,.L"Q, t r '- 't !.,'dh
b. SO cm
c. 70 cm
d.50cm
e. 20 cm
~
O.2..=-
(>-
0,( to.L
:: !:..U;tJ
=O,70~l:A.:)
20. Your physics teacher has a mass of SO-kg while holding his calculator, 3-ring binder, pens, and grade bo .
He is forced to walk the plank by his unruly c1asses ...the plank is 4.0-meters long and sits atop the lab bench.
The 4.0-meter long plank has 0.5-meters extending past the bench and 3.5-meters still above the bench. While
standing at the very end of the plank your teacher just balances. What is the mass of the plank?
~====~a.
b.
c.
d.
e.
24.7 kg
11.4 kg
26.7 kg
20 kg
10 kg
~
r~
£T--;0
:: (~,
X
F"; )-
t, F:j + 6 X F;J
X
C-26.7kg or 261N
6.
Determine
arc length, angular
22. The rotational
velocity,
velocity of a 45 rev/min
a. 45 rad/sec
b. 283 rad/sec
c. 0.75 rad/sec
d. 4.7 rad/sec
e. 15.7 rad/sec
and angular
record in radians/sec
rYS (Jd,..)!
~..,.{)
"-,I" l
\.
acceleration.
rev
is approximately:
I~ \ _
lbo,,,,) - 1.(, 7
II
(o..(/!~~c.
D -4.7rad/sec
24. The armature of a motor is accelerated uniformly from rest to a rotational velocity of 1800 rev/min in 10.0
seconds time. The rotational acceleration of the motor is:
6, ()j ~ I tf;O!.9- - ()
01 ~/&J(jt'Y .
W
r- 0
<: IO.o~
a. 180 rad/sec'
b. 90 rad/sec'
c. 37.7 rad/sec'
I\-\.l\
~l~
=
f
0<. ~ ~
d. 18.8 rad/sec'
D-l8.8rad/s
7. Demonstrate
'8'y.
V !!:i'>.(t~
'-U .h Y4J )7-#\1
f$t}
~
l"
188.!>'s04
-=-
.6.t
2
~
/08.$ ~_,
- I{).O~
conceptual knowledge of moment of inertia and how it is affected by changing mass
distribution
27. When a gymnast moves from an extended position to a tucked position, she
_
a. decreases her moment of inertia
b. increases her moment of inertia
c. neither a or b
A-r decreases m stays the same.
28. A short pendulum has a larger moment of inertia than a long pendulum of the same mass.
a. T
L
T"
b. F
False-a smaller one m is the same r is less.
'('I\t
, ,.:
de<",~e.s.
-'<".,.
29. Dancers may change their moment of inertia while going through a break-dance routine.
a. T
b. F
True: change r for arms and legs.
1) The condition for rolling without slipping is that the center of mass speed is
A)
Vcm
= ro/
B) vem =2raJ
raJ
C) vem =-2
D) vem
= raJ
E)
= r'aJ
Vem
Answer: D
Diff: 1
3) A 50. cm diameter wheel is rotating initially at 2.0 revolutions per second. It slows down uniformly
and comes to rest in 15.seconds.
V2
(a) What was its angular acceleration?
~
2.I'eIJ
2
~~
J,.
e.v -\.O -
2
Answer: (a) -0.13 rev/s
Diff: 3
;
2
-0.84 rad/s
At':..
\ ( ,
)
A - ~.J.-
If~
OZ := ~
£H
:-
-12.. (, '1c~
1$;1,,"4
(\
4) A wheel of diameter 0.70m rolls without slipping. A point at the top of the wheel moves with a
tangential speed 2.0 m/s.
(b) What is the angular speed of the wheel?
Answrg'
b).
Diff:3
_
Is
v~ru.)
e.u ':: 3d._
r -
r 'k \;."ll
0.(.
MA-l<..
'*-~"a..v ~~ ~4
Answer: A
Diff: 1
6) A wheel slows down uniformly and comes to rest in 15. seconds. It is rotating initially at
2.0 revolutions per second and has a diameter of 50.cm.
f': 6~
"'2.-
(b) What was the tangential acceleration?
{. ":: (3.5
Answer:
(b) -0.21 m/s2
L\CU=
Diff: 3
o ~ - @ ,Offl''j.2-7{
q :.r cJ.. :: 0 2. ~'"
7) A cylinder, of radius 8.0 em, rolls 20.cm in 5.0s.
::::-~
(a) Through what angular displacement does the cylinder move in this
(b) What is the angular speed?
r-::.
0, 0 8 6""
J ': 0,2-0
Answer: (a) 2.5 radians (143°)
(b) 0.50 rad/sec
Diff: 2
r =-
r,O,
IV\
,2. I 'of
!
Y 7i: "':Y1)
I S-~5G..
Q:."<
d=r8
e : cfr
8) A bicycle is moving 4.0 m/s. What is the angular speed of a wheel if its radius
A) 4.8 rad/s
6 130'"\
B) 7.6 rad/s
L{.OM~
C) 0.36 rad/s
D) 1.2 rad/s
7
E) 13. rad/s'
r':.
0-
~TI
~ ,20"L~ z.(Nltii/
oPo•.l._...
-__ -/'
is 30.cm? 0 _I> ()
- ~
lJ ::
V ::
Answer: E
Diff:2
"t
.•
2.r;~
-.--,OJ
:s
to/fret
1) What condition or conditions is/are necessary for rotational equilibrium?
A)
L~=0
B)
LF =O,LF =0
C)
2>=0
D)
IF
E)
IF, = O,LF,. =O,I, =0
y
x
x
=0
Answer: C
Diff: 1
2) A girl weighing 450. N sits on one end of a seesaw that is 3.0 m long and is pivoted 1.3m from the
child. I! the seesaw is just balanced when a boy sits at the OR osite end, what is his weight? N:.glec:@{t ~
the weight of the seesaw.
r-:t:. '\ ~ - \
I
L:: 0
1:--7 <!:
Answer: 344. Newtons
Diff:2
')
L .)'"'1
I.7""
~~-:iF;
tFt
5) Five forces act on a massless rod free to pivot at point P.
I-~)
;;..
:ocr,
Illj
~~'"
o -(S-BS"'J'1 +-0. 7", ~ j
$"~"'"
;,0
I, 7,.j
A
A)A
@
E)E
Answer: C
Diff: 2
(out of th,$-Paper) torque about point P?
~
-~
r-)
(;X~)J
=~.3 W\YrSDIJ)jt~foj1 t rln..:(Ft
Fl..
3'N.N~h..
Which force is producing a counter-clockwise
~
~1
9) A boy and a girl are balanced on a massless seesaw. The boy has a mass of 60 kg and the girl's
mass is 50 kg. If the boy sits 1.5m from the pivot point on one side of the seesaw. where must the girl
sit on the other side for equilibrium?
A) 3.0 m
~
~~
~
D) 1.8m
I
f
C:=//
rl
<!?
'-9i'
-h &..;.
\ "=' nQjJ
'(~"'-.J -..Joo
Or
jJ.1.
r, =&D':I:lr.n~
>
L
r0
~II;J
,,;,,;:4- <?
j)
f. q:= 0:. 't r.) ~t.~
')( }{dF;y
_
f
I:
f
Answer: D
Diff: 2
10<:",
"t ~
7
'
/
t/ •• t
r,
~( -.
,
I'l
~l
,I
r; f,'sIAfO.E (, r, SA'/do')./'
f, F, ::. r •. r-to. ---'
:;>
r,-•..:: ,j.~Q
('
t-.. ~
6) A uniform rod has a weight of 40.N and a length of 1.0m. It is hinged to a wall (at the left end), and
held in a horizontal position by a vertical massless string (at the right end).
string
~,~;/1--_
~
~
1
....
fUll""
~
hinge
z;.rc=-o ~(j!1)~t )(;0
rod
wall
t\
F, si...e,
-::-"'. 'F,
~in.&L
CD.~My''10 t-J'}.SI'''? ~
="l::a- ~ 2.0~;;;J
What is the magnitude of the torque exerted by the string about a horizontal axis which pa~s
through the hinge and is perpendicular to the rod?
A) 40 N-m
B)10N-m
:..;.;
)
5 .N.
Jt!i
20 N-m
):BO- -m
Answer: D
Diff: 2
8) What condition or conditions is! are necessary for static equilibrium?
A)
IF,. =0
B)
IF, = O.IF, =0
C)
Ir=O
D)
IF,
=0
IC
E)
IF, =O.IF, =O.Ir =0
f3~J
l\.Ot
aC(el~'h~
1\ eL~lI.¥"
~t\f\.
~
"tra..V\Jt 'hON!.
I.
Answer: E
Diff:2
10) A heavy boy and a lightweight girl are balanced on a massless seesaw. If they both move forward
so that they are one-half their original distance from the pivot point, what will happen to the seesaw?
A) It is impossible to say without knowing the masses and the distances.
9 ~
e-side the bQ~~:~ng
on wil! lilt downward.
I'
C Nothing, the seEL
ill-still-Ge-balancea.~
(.L::- ()
S1~ r ~
~'A(j
D)
e Side the girl is silting on will lilt downward.
I I
I
~ Z.
l..
--rzr
=- r /-
Z-
r;
Answer: C
Diff: 2
11) "Lever Arm" can have which of the following units?
(a) Joules
(b) N.m2
(c) kg.m2/s
(d) kg.m / s2
l@ITetersO:::>
Answer: (e) meters
Diff:1
13) A force is applied to the end of a 2.0m long uniform board weighing 50.N, in order to keep it
horizontal, while it pushes against a wall at the left. If the angle the force makes with the board is 30°
in the direction shown, what is the applied force F?
r\.'::
2...0 ""
F
1""::?
r'2,.
A)
B)
C)
D)
E)
,
SL,,30'
58.N
50.N
29.N
90.N
32.N
r l,~
f \"SOl--'
l'"
~
£':C={r,x
Answer: B
Diff: 2
Fj-'r\)(~.j
~\,,-e,':: r, F, SlA9't
f, r, ~1"fO. ., F~
'I, f,
8.3 Rotational Dynamics
"'.6'''''!oj ~
3) Torque has which of the following units?
.
(b)
c
(d)
(e)
s
Nm
g m2/s
kg m2/s2
kg m2
Answer: (b) N m
Diff:1
r
4) A 2.50 kg is at (r1.00, 3.00)
(a) about the x-axis?
(b) about the y-a . .
(c) about the Ii de.
Answer: (a) 2.
(b) 2
(c)
Oiff: 3
5) Is it easier to swing a bat holding the handle at the end, or "choked up"? Why?
Answer: "Choked up", because the moment of inertia is less about the axis of rotation (bat center of
mass moved toward axis).
Oiff: 2
6) Consider a solid object which is subjected to a net torque. That object will experience which of the
following?
A) a Ii
r accele
d an angular acceleration <t!- """"-'\
I
{\.Oi-- () r ("fAvo...
an an ular acceleration
...J
I I.I'a .:l_ ••.
b~
C) a constan
r ve ocity "0) a changing moment of inertia~
Answer: B
,."J.
t-j 0 \
$0 \
b
0
Joe.(..
t- -
f'..D
bur
ct,,,
.. c..
F"""'-V'j
/ f\
I.,
o iff: 1
B)
C)
0)
E)
-zero tor
s
ular acceleration.
mo en um.
angu
velocity.
angular
omentum.
moment 0 ertia.
Answe2-i
Oiff: 1
A
14) An ice skater performs a pirouette (a fast spin) by pulling in his outstretched arms close to his
body. What happens to his moment of inertia about the axis of rotation?
A It doe
t change.
It decreases
C) It Increases.
0) It changes, but it is impossible to tell which way.
Answer: B
Oiff:2
. ,.
•
16) A solid cylinder and a hollow cylinder have the same mass and the same radius. Which statement
is true conc
. their mo
f-iRema-aeett!-a'
rough the exact center of the flat surfaces?
The hollo ~cylinder has the reater moment of ine I
e solid cylinder has the greater momen 0 me la.
C) Both cylinders have the same moment of inertia.
D) The moment of inertia cannot be determined since it depends on the amount of material
removed from the inside of the hollow cylinder ..
Answer: AI::
Diff' 2
M
r 1..
.
f'\.Of'e. fV"vll..~
~J tt. 4"I'€al-u
V\AOMen t cI
"j
If
q Ita--tel""
dis.
t
'H\L€
Il\.evh'ct
'
. •
I
20) Consider two uniform solid spheres whereboth have the same diameter, but one has twice the
mas~er.
The ratio of the larger moment of inertia to that of the smaller moment of inertia is
2.
O.
C)4.
.-:--\
-
J.- -
D) 8.
E) 6.
'(V\.
eL
'fY\ .•.. :=1~.
Answer: A
Diff:2
2 W\,
OY'& '/
JY()e~~r
23) Moment of Inertia has which of the following units?
(a) joules
(b) N.m
(c) kg.m2/s
~~
..22
~
Answer: (e) kg_m2
Diff: 1
4) An 82.0 kg painter sta~~~~~oard
1.55m from one end. The 15.5 kg board is
5.50 m long. The board is supported at each end.
(a) What is the total force provided by both supports?
(b) With what force does the support, closest to the painter, push upward?
Answer: (a) 956. N
(b) 653. N
Diff: 3
.f
1
s,
~2-