Essential University Physics, 3e (Wolfson) Chapter 11 11 Rotational Vectors Vectors and Angular Momentum
1 1. 1 Co nc e pt ua lQue s t i o ns 1) If two vectors are perpendicular to each other, their cross product must be zero. A) True B) False Answer: B ar: 1
!) If two vectors point in opposite directions, their cross product must be zero. A) True B) False Answer: A ar: 1
") If
and
are nonzero vectors for which
A)
$
B)
is parallel to
&) '
$
| % AB.
() '
$
| % 1.
∙
= #, it must follow that
% #. .
Answer: & ar: 1
) As *ou *ou are leavin+ a buildin+, the door opens outward. If the hin+es on the door are on *our ri+ht, what is the direction of the an+ular velocit* of the door as *ou open it A) up B) down &) to *our left () to *our ri+ht -) forwards Answer: B ar: 1
) /hen *ou ride a bic*cle, in what direction is the an+ular velocit* of the wheels A) to *our left B) to *our ri+ht &) forwards () bac0wards -) up Answer: A ar: 1
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2) The an+ular momentum of a s*stem remains constant A) when the total 0inetic ener+* is constant. B) when no net e4ternal force acts on the s*stem. &) when the linear momentum and the ener+* are constant. () when no tor5ue acts on the s*stem. -) all the time since it is a conserved 5uantit*. Answer: ( ar: 1
6) A metal bar is han+in+ from a hoo0 in the ceilin+ when it is suddenl* struc0 b* a ball that is movin+ horizontall* 7see fi+ure). The ball is covered with +lue, so it stic0s to the bar. (urin+ this collision
A) the an+ular momentum of the s*stem 7ball and bar) is conserved about the hoo0 because onl* +ravit* is actin+ on the s*stem. B) the an+ular momentum of the s*stem 7ball and bar) is not conserved because the hoo0 e4erts a force on the bar. &) the an+ular momentum of the s*stem 7ball and bar) is conserved about the hoo0 because neither the hoo0 nor +ravit* e4erts an* tor5ue on this s*stem about the hoo0. () both the an+ular momentum of the s*stem 7ball and bar) and its 0inetic ener+* are conserved. -) both the linear momentum and the an+ular momentum of the s*stem 7ball and bar) are conserved. Answer: & ar: 1
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1 1 . 2 Pr o bl e ms 1) /hat is the vector product of
% !.## 8 ".## 8 1.##
and
% 1.## 9 ".## - !.##
A) 9".## 8 .## 9 .## B) 9.## 8 !.## 9 2.## &) 9.## 9 ".## 9 ".## () 9.## 8 ".## 9 1.## -) !.## 9.## 9 !.## Answer: A ar: 1
!) /hat is the ma+nitude of the cross product of a vector of ma+nitude !.## m pointin+ east and a vector of ma+nitude .## m pointin+ "#.#; west of north A) 2." B) 92." &) .## () 9.## -) <.## Answer: A ar: 1
") If the ma+nitude of the cross product of two vectors is one9half the dot product of the same vectors, what is the an+le between the two vectors Answer: !2.2; ar: 1
) If
% 9 9 ! 9 " , what is
$ ?
A) 8" 9 B) 8" 8 &) 9" 8 () 8" 8 ! 9 -) 9" 9 ! 8 Answer: A ar: #8
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) If
% 9! 9 2 8 ! and
ma+nitude of
$
% 9! 9! 9 " , which of the followin+ numbers is closest to the
A) ! B) !1 &) 16 () 1" -) Answer: A ar: #8
2) For the vectors shown in the fi+ure, find the ma+nitude and direction of the 5uantities shown are accurate to two si+nificant fi+ures.
A) !2, directed into the plane B) !2, directed out of the plane &) "1, directed on the plane () "1, directed into the plane -) "1, directed out of the plane Answer: A ar: 1
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$
, assumin+ that
6) For the vectors shown in the fi+ure, find the ma+nitude and direction of the vector product $
, assumin+ that the 5uantities shown are accurate to two si+nificant fi+ures.
A) 12, directed into the plane B) 12, directed out of the plane &) , directed on the plane () , directed into the plane -) , directed out of the plane Answer: ar: 1
<) A force
% ".## = 9 !.## = acts at a location
% 1.## m 8 !.## m on an ob>ect. /hat is
the tor5ue that this force applies about an a4is throu+h the ori+in perpendicular to the xy9plane A) 91.## =?m B) 6.## =?m &) 9".## =?m () .## =?m -) 9<.## =?m Answer: ar: 1
) /hat is the tor5ue about the ori+in on a particle located at % " m %= 9!= 8"= A) 7< 8 9 !2
) =?m
B) 7< 9 1 9 !2 &) 7< 8 ! 8
9! 8
) =?m
) =?m
() 712 9 1 9 !2 -) 7<
acts on the particle
) =?m
) =?m
Answer: B ar: 1
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8m 9!m
if a force
1#) Three solid, uniform, c*lindrical fl*wheels, each of mass 2.# 0+ and radius 1.6 m rotate independentl* around a common a4is. Two of the fl*wheels rotate in one direction at the other rotates in the opposite direction at " .! rad@s. &alculate the ma+nitude of the net an+ular momentum of the s*stem. A) !< 0+?m!@s B) 66< 0+?m!@s &) !6 0+?m!@s () !!! 0+?m!@s Answer: A ar: #8
11) A potters wheel, with rotational inertia is spinnin+ freel* at # rpm. The potter drops a lump of cla* onto the wheel, where it stic0s a distance 1.! m from the rotational a4is. If the subse5uent an+ular speed of the wheel and cla* is "! rpm what is the mass of the cla* A) <.# 0+ B) . 0+ &) 6.# 0+ () <.< 0+ Answer: A ar: "<
1!) A bic*cle is travelin+ north at .# m@s. The mass of the wheel, !.# 0+, is uniforml* distributed alon+ the rim, which has a radius of !# cm. /hat are the ma+nitude and direction of the an+ular momentum of the wheel about its a4le A) !.# 0+?m!@s towards the west B) .# 0+?m!@s verticall* upwards &) !.# 0+?m!@s towards the east () .# 0+?m!@s towards the east -) .# 0+?m!@s towards the west Answer: A ar: 1
1") A ##9+ particle is located at the point
% m 8 "m 9 !m
and is movin+ with a velocit*
% m@s 9! ms 8 m@s . /hat is the an+ular momentum of this particle about the ori+in A) 7! 9 2 9 < ) 0+?m!@s B) 71! 9 " 9 ) 0+?m!@s &) 7< 8 1 9 1" ) 0+?m!@s () 71# 9 8 ! ) 0+?m!@s -) 7 9 1" 9 11. ) 0+?m!@s Answer: ar: 1
1) A fi+ure s0ater rotatin+ at .## rad@s with arms e4tended has a moment of inertia of !.! 2 &op*ri+ht !#12 3earson -ducation, Inc.
0+?m!. If the arms are pulled in so the moment of inertia decreases to 1.<# 0+?m!, what is the final an+ular speed A) !.! rad@s B) .2# rad@s &) 2.! rad@s () 1.62 rad@s -) #.<1# rad@s Answer: & ar: 1
1) A .#9m radius pla*+round merr*9+o9round with a moment of inertia of !### 0+?m! is rotatin+ freel* with an an+ular speed of 1.# rad@s. Two people, each havin+ a mass of 2# 0+, are standin+ ri+ht outside the ed+e of the merr*9+o9round and step on it with ne+li+ible speed. /hat is the an+ular speed of the merr*9+o9round ri+ht after the two people have stepped on A) #.!# rad@s B) #.# rad@s &) #.2# rad@s () #.<# rad@s -) #.26 rad@s Answer: B ar: 1
12) A record is dropped verticall* onto a freel* rotatin+ 7undriven) turntable. Frictional forces a ct to brin+ the record and turntable to a common an+ular speed. If the rotational inertia of the record is #. times that of the turntable, what percenta+e of the initial 0inetic ener+* is lost A) " B) 1< &) 2 () 2# Answer: A ar: #8
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16) A turntable has a radius of #.<# m and a moment of inertia of !.# 0+ ? m!. The turntable is rotatin+ with an an+ular velocit* of 1. rad@s about a vertical a4is thou+h its center on frictionless bearin+s. A ver* small #.#90+ ball is pro>ected horizontall* toward the turntable a4is with a velocit* of ".# m@s. The ball is cau+ht b* a ver* small and ver* li+ht cup9shaped mechanism on the rim of the turntable 7see fi+ure). /hat is the an+ular velocit* o f the turntable >ust after the ball is cau+ht
A) !.1 rad@s B) 1." rad@s &) #. rad@s () #.6 rad@s -) #."# rad@s Answer: B ar: 1
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1<) A turntable has a radius of #.<# m and a moment of inertia of !.# 0+ ∙ m!. The turntable is rotatin+ with an an+ular velocit* of 1. rad@s about a vertical a4is thou+h its center on frictionless bearin+s. A ver* small #.#90+ ball is pro>ected horizontall* toward the turntable a4is with a velocit* of ".# m@s. The ball is cau+ht b* a ver* small and ver* li+ht cup9shaped mechanism on the rim of the turntable 7see fi+ure). The percent of the initial 0inetic ener+* of the s*stem that is lost durin+ the capture of the ball is closest to
A) . B) 1. &) . () 2#. -) 2. Answer: B ar: 1
1) A uniform dis0 has a mass of ".6 0+ and a radius of #.# m. The dis0 is mounted on frictionless bearin+s and is used as a turntable. The turntable is initiall* rotatin+ at "# rpm. A thin9walled hollow c*linder has the same mass and radius as the dis0. It is released from rest, >ust above the turntable, and on the same vertical a4is. The hollow c*linder slips on the turntable for #.!# s until it ac5uires the same final an+u lar velocit* as the turntable. /hat is the final an+ular momentum of the s*stem A) #."
@s
B) 1.1
@s
&) 1."
@s
() 1.2
@s
-) 1.
@s
Answer: A ar: #8
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!#) An ob>ect is rotatin+ with an an+ular momentum .## 0+?m!@s
while bein+ acted on b* a
constant tor5ue ".## =?m . /hat is the an+ular speed of precession of the an+ular velocit* of the ob>ect A) 1."" rad@s B) #.6# rad@s &) 1!.# rad@s () zero -) It depends on the moment of inertia of the ob>ect. Answer: B ar: 1
!1) In the fi+ure, the rotor of a +*roscope is a uniform dis0 that has a radius o f 1".< cm and a moment of inertia about its a4is of .# $ 1#9" 0+∙m!. The len+th of the rotor shaft is 2. cm. The ball pivot at P is frictionless. At a +iven instant, the rotor shaft is horizontal and the rotor is rotatin+ with an an+ular velocit* of # rad@s about its a4is OP , as shown. The rotor is viewed from point Q on the a4is. The precessional linear velocit* o f point O, includin+ the direction seen from point Q, is closest to
A) #.# m@s, leftward B) #.# m@s, upward &) #.# m@s, ri+htward () #.11 m@s, downward -) #.11 m@s, ri+htward Answer: A ar: 1
!!) 21) A bic*cle wheel of radius #."2 m and mass ".! 0+ is set spinnin+ at .## rev@s. A ver* li+ht bolt is attached to e4tend the a4le in len+th, and a strin+ is attached to the a4le at a distance of #.1# m from the wheel. Initiall* the a4le of the spinnin+ wheel is horizontal, and the wheel is suspended onl* from the strin+. /e can i+nore the mass of the a4le and spo0es. At what rate will the wheel process about the vertical A) !. rpm B) 1. rpm &) 1< rpm () #."# rpm -) #.66 rpm Answer: A ar: 1 1# &op*ri+ht !#12 3earson -ducation, Inc.
