A bicycle odometer (which measures( 0oz(nopo7q-va)ww e distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch oo0n(p wz v)ea(-owq7wheels?

Suppose a disk rotates at coi c3p wf karg(b5pd9/(nstant angular velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the poipwcb9r3p/f igka5(d( nt have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a si g sz-5hsofh)s6a131qd9n jepy wl 7 f,k2fg7sngle value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a dfqvma+b e/(9 larger force? Explain.

If a force $\vec{F}$ acts on an object such that its lever arm is zero, does it have any effect on the object’s motion? Explain.

Why is it more difficult to do a sit-up with your hands behind your head tqkt6m / wvy2m+ (pg0ithan when your arms are stretched out in f2mp(yt+v 6qw m t0g/kiront of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at the6viuhf+ q28 ijp/l2sw pedal cranks. In which gear is hs w2iv/i6 2uq8+pjlf it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender ck5ohq+ jbtk7jmd(61 ;eo m(plower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the bqm+c7dkooj (6h e;kp m15( jtbasis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (F geea9/zb :o:big. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is tbn8r2*/m4y 3ibsxi )tzgq nz0he net torque also zero? If the net torque on a system isiyz*mzg2n /qix bn 8t4r b30)s zero, is the net force zero?

Two inclines have the same height but make different gqpo4d 29,;m7e* z8k-miegfdpt:rs langles with the horizontal. The same st ep*4 2f87 :l-esp;9dd,mmiqogtkzgreel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolli4. 6z)oh./du zmos alpng (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total k os).h mzdpuao6zl/.4 inetic energy at the bottom?

A sphere and a cylinder have epnyq 5 z 2cw4ly)xe,/ l9yzw+the same radius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kiynl4xyezp5 9ew2+yw,cz lq)/netic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most 2/*7.pd(upcp mocnsymoving or rotating objects eventually slow down and snp7psd*c y/ op m.(cu2top. Explain.

If there were a great migration of people toward the Earth’s equator, how wge)we--ftj+v;8pm mf ould this affect th-;g8te )v+ fjpwm emf-e length of the day?

Can the diver of Fig. 8–29 do a somersault without having any initial rotati 9)-o*+zvtaj5f c im3a mq6 6t fskg)mghplk38on when she leaves the boardtp68v-mfg)9k a l5+3iozscj6g)q*3 atmf hkm?

The moment of inertia of a rotating solid disk about an axis thj/eiqr2t+9m orough its center of ma9 j+/otq er2miss is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holding a 2-kg m,len v y+lp)1fass in each outstretched hand. If you suddenly drop the masses, will your angula+ln1ef) yl ,pvr velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is hollow as1xf/ gbb .1n t7uko;ind the ok.1bgsi t7f;o/1 b uxnther is solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle z0cfkz9tz5ys : -dr v;points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration poi5-z9zvt :yfz 0sc;rkd nts east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotde0s-6r9 c ip(yge ;juating turntable. What happens if you walk towe;9 s dgy rpe0ujc(i6-ard the center?

A shortstop may leap into the air to catch a ball and throwwkxu4 j- ay .wc.ssa25 it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will.w4-5 c.sa2s ajuwyk x notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angdrjbau49 :*o4rpi * mtular momentum, discuss why a helicopter must have :4*4parbmujt oir9 d*more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians: (a) j 6wp mgon2g wk5;ckb7leg *e965iq*h30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coincidence. Calculatcz,+r(o+sj*u0ew k tg-o)pr h e, using the information inside the Front Cover, the angular diameters (in radians) o0o *e)tz ksc+ (ru +jr,wogp-hf the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the fd q:*; -xgyoffgy -t.Moon, 380,000 km from Earth. The beam diverges at ay:t;gd--o fqfg xf*.y n angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. When the motor is turn ,cyvs u(65a./i g:mejdgwos(lkk(, b ed off during operation, the blades slow to rest in 3.0 s. What is the angular acce egajo,ckl(ud.5/:s(wkms gy v6, bi(leration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a 3eo2p 2im:hut level floor 3.5 m to another child. If the ball makes 15.0 revolh2 omeu:i pt23utions, what is its diameter?    m

  A bicycle with tires 68 cmg51co ci9n53e5be g grz4rk w; in diameter travels 8.0 km. How many revolutions do the wheels makengcz1; ec4wo 59 5b g53eirrgk?    $rev$

  (a) A grinding wheel 0. -igs3jwd :y0e35 m in diameter rotates at 2500 rpm. Calculate its angular velocity di- yseg3 jw0:in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolution in 4.0 ha l.)wr;8g 1dr4gkpm s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m fr4 k 1hm.8)gr;rdlapwgom the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in its orbit arou)rf r8nnja.+j5 gpiv ,nd the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a*0jn d,lx jbq(sffv(apl2 ,a 9 point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 cm from the axishjs e 6;8p v-h+ebeql4 d1 o94:8vueo inh3syc of rotation is to experience an acceleration of 100,000 yb1 v4e hju4e9 68h:o dsei38ql-c nseo;hv +p$g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center fr6c1 tl-ruveq6 om 130 rpm to 280 rpm in 4.0 s. Dete 1uq6-e6ltr vcrmine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radius (ui;dwri lh /5$R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$

  In traveling to the Moon, astronauts aboard the Apollo spacecraft put themselveql0k3t0zp p r*b81 p7 s3t9-nzgokbpfs into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerag-nb0k 3zsp po* qptrk01fz bt937l8pted from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm in 220 l:r ;.boa0jtw 2axkp,s. Through how many revolutions did it tu aj.bokr2x,: lpt;0a wrn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s.0 ;s-tk. 0yzbotvtp :t Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jets if.mh sm+4;p)ua h *ifnj2d8 3-pjpkoc n a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complf 8 2uc;3ka 4jmho ds)nfpi+-.jmp*ph ete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter 5mtd+j7daon bo 1g9;igf/.o a(qi gv2 accelerates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in this1(o g aa7 fibq5 n.v/ oio29dgd;+mjgt time?    m

  A cooling fan is turned off when it is running yuqzbr5)+*:lqmg+ s s6ue ce 7at 850rev/min It turns 1500 revolutions before it comes to m q c sqle5uzs*7y6u+):+brge a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed unifi(r)x, .olihbi r)b8tj08 cfzormly from 95km/hxtrzji8,8 0)hi f)b i.(ocrbl to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the c4o-phcqye jm7+h n2( car reduces its speed uniformly from 95km/oej y4nqh-hp7c2(+cm h to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all hwrds+k fv (r:3cp9a7 qer weight on each pedal when climbing a hill. The pedals rotate in a circle of radius 17dp:wr+a( k7f 9qscv3r cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 nslr f3-wxz8bsm: h23cm wide. What is the magnitude o3 mlx-hf2swznr 8s 3:bf the torque if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel shown in Fig. 8–39. Assume u.2n*czse o8 othat a friction torqueezsuc8.o*n2o of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, aragdhaom3k7sw 3 42hb8e attached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then re7akdog3wbs8h a2m4 3h leased. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine 33zaiau- e5h :xi gas8xo6m6 srequire tightening to a torque of 38 es66: 8aag xa zui-53o 3mshix$m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-kg sphere of radiuy2u6*mun :a.iw b- ysvs 0.648 m when the axis of rotation is through yu.sv:* -wub 26yimnaits center.    $kg \cdot m^2$

  Calculate the moment of dzg y++/)hj 6n btzs;einertia of a bicycle wheel 66.7 cm in diameter. The rim and tijegnzz t 6s+y)dhb;+/re have a combined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in a h3j znw. i7m zari,k*2tlv(zi5orizontal circlez5.lkt ij(23mz7 wnaiv*i z,r of radius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rotating at constant angulx*ug0,/ f sg;rqe 2uoaar speed (Fig. 8–42). The e2 af/0g,r; *suo gxuqfriction force between her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertiam+yw k 1;4baq*ub 1vpu of the array of point objects shown in Fig. 8–43 abouk+u1 ubm4yq1bva; p *wt
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxygen atoms whoseempi(c satur:b8 ;d,ug7,+j t total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinni4fxecc8u ylhn/ 5qkc2ioi- e6 9k:6 rcng at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satu9 ccq6o6ef4ycrxi5e l ik 28-ckh n/:ellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm and a mass of 0 26jc rm,akgl(jf/d 4ih2,;)wlezjzm qt7 ;sv .580 kg. Calculate jm(/v)2 w zgqaf llm7i s;2j;thj4ezk dr,, c6
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, ey 6+a3l);iytbpz j71 :uulipxb m:8g accelerating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-driven merry-go-ror* 4;c :yualibhi4c1 l-ns*c.xoxx6 gund and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-gicy4l*lxh1s rb;co x. an-x:c6 giu4*o-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and lk3*1ed,r eq eis eventually brought uniformly to restede*13r qkel, by a frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a 3.6-kg bj// ymm l.h uc61le,ik8idy o9kr,c8 hall at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action of the forearm, wr;3r ;nj y-bv;meo t:phich rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly fromor:;pmjyne t;v ;3-br rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade caa9q17iimrizk:; bs9 kn be considered a long thin rod, as shown in Fig. 8–46. 9:k1ai;q9bmz7i rk si
(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.    $kg \cdot m^2$
(b) How much torque must the motor apply to bring the blades up to a speed of 5 $rev/s$ in 8.0 s?    $m \cdot N$

An Atwood’s machine consists of two masses0o/r1spbp/ d(p++v* 3pbb yy8grdo qc, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest within fo(b w4jb3 g z f0ygb5rh4kka)8cur full turns (revolutions) and rg)k3f y54hkg4b 08 (w zabcrbjeleases it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of inertia of ,cd5l j94 ed3fpejqst +w2q* o0nj r7r$3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a :b6q0p(pw:oqm tff4ytorque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius p/m . eob.nnu*0 d;jq;xy* 85ynh pzbf9.0 cm rolls without slipping down a lane at ;/yz.h b;n* m.nnyfx pu8qpe5j0*od b 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth /m0nh j lz,atxk 9 g40stja:r ,2kuv;pyxxf-0with respect to the Sun as the sum of twot : 00h/xjkmj ztul;4vxpxrk-f,n 9s0g2 ,a ay terms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius ofof)npzim+j2 hh 1k6a ) 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cyli+pia)ok m2f) 6jh1hnznder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and rolld0,5yr/agx v/(uscu p(b xi4 ls without slipping (dui(clx yg4ruvb0x,/ sa/ 5pdown a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

  Two masses, $m_1$ = 18 kg and $m_2$ = 26.5 kg are connected by a rope that hangs over a pulley (as in Fig. 8–47). The pulley is a uniform cylinder of radius 0.260 m and mass 7.50 kg. Initially, is on the ground and $m_2$ rests 3.00 m above the ground. If the system is now released, use conservation of energy to determine the speed of $m_2$ just before it strikes the ground. Assume the pulley is frictionless.    $m/s$

  A 2.30-m-long pole is b::(eycl m01. d/mbzd edt6ccwalanced vertically on its tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: U/6:1dmzdwb cedt el .(0y m:ccse conservation of energy.]    $m/s$

  What is the angular momentum of a u4 yaoq5j2r( t0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an angular speed of 10.(q yrjoa5t24u4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindricaj)szdn/3b d8i, sgvv3f 5 3ognl grinding wheel of radius 18 cm when gj85) 3gfzs3dnvb/ni v,dso3 rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that is rotating h/.jgidll2z5(2eye-8u jmq y at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed ofedzqeyui2y( 2l l5. /-j jghm8 rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) c1(,9ld tjua 4i fgz*cran reduce her moment of inertia by a factor (lr9 fazugjc14t* d,iof about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial rate .t.oc hrod;n-q/ cl;l of 1.0 rev rnoq-lt . o/c c.dhl;;every 2.0 s to a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rc rrib (f3 7sucy*s)l/otating around a vertical axis through its center at a frequency of 1.5rev/s The wheel can be co7b/ )(s cu*lryrcs3 ifnsidered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure slb+ -bn ykcnq4ie4sfm p fp0 ((h*iv18kater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of the Earph/ft: i8357 vbfizmfth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$

(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inertia I is dropped r04vsxw n-0u2cqi g5 ionto an identical disk rotating at angular sp-cu0wr xiiqg0 v54ns 2eed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.43p8gtxl / r6xe $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stand tqc a 8*9s9 7s2dnfv3p.jomj wq- /3ag6yrzsis at the center of a rotating merry-go-round platform of radius wm/qipctd-28gs.z sjs6 *a7v r jan3yq 399fo 3.0 m and moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round 9ss-.mwhobkml::sh 0xjc dz9w3 0db +is rotating freely with an angular velocity of 0.8z90bxw9sbkls d:d.h0o 3w j-c mm+hs: $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventuallcj 7t; scdt ynf+8zh2(y collapses into a white dwarf, losing about half its mass in the process, a f+8y(c chz7sj n;t2tdnd winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve windshnaco+v w d5mw.6z 8269 isiz(hy:..v pqdftx in excess of 120 $km/h$ at the outer edge. Make a crude estimate of
(a) the energy,    $ \times10^{16 }$ J
(b) the angular momentum, of such a hurricane, approximating it as a rigidly rotating uniform cylinder of air (density 1.3 $kg \cdot m^2$) of radius 100 km and height 4.0 km.    $ \times10^{20 }$ $kg \cdot m^2$

  An asteroid of mass )(fj pyy x.o.2stk 8hn$ 1.0\times10^{ 5}$ traveling at a speed of relative to the Earth, hits the Earth at the equator tangentially, and in the direction of Earth’s rotation. Use angular momentum to estimate the percent change in the angular speed of the Earth as a result of the collision.    $\times10^{-16 }$ %

A person stands on a platform, initially at rest,e)uv6qh fxl(oi5x)pe)i /-ez that can rotate freely without friction. The moment of inertia of thh)ie-)e)q efux 5pz6ilo/x (v e person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stnozm il 9 j.2a64n6(fe4jq epzands at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of inertj6 46zepo2ezlfi49aq j(. nmnia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the ez4rc9fyu* x0r 3urb 1cnd of the rope lying on the top edge of the spool. A persoczxu0uy rf*9 r 4b1r3cn grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always z)tq(/ 1dtm ccfaces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat ccm(1 dqt )zt/the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rauu;ohd(c t9 y2 r3o.er9z8tyr te of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone ina5-sl ;kxn4ttq : rwax3 q-2de the shape of a uniform cylinder of radius 0.20 m acquires a rotationaa:q ate;qrnsx5-3d4lx-kt2w l rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, eac ldgq.u7 ;oc *:a4rmqah of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long mo.agqr:u; 7qd *lac 4string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the a9 6/*l0ao ql zp rxen3b/w3cylngular speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, z +-r dd)nmo,/w2ahshbut with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collsno)mh a-w,/+h2rdzd apse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is f1pcb+wj5rc 1xe4,jui or it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km withouw b jec 45ir11jx+cp,ut needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrate n9dpkp52k -kqs an $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizontal surface at speed v=3. :+gk(bkvy4 j ft3ikt(3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (i.e., lp8 z9shajk2*(y uwa/ we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration ofwpz a (jhsl/y9a*82 uk the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standl3t6ze i8 sv eb8*b5going vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55*b8e 36getzbosl5i 8v ). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a f, tyabz,rffv 7ps:l+8 lat road is making a turn with a radius The forces acting on the cyclist and cycle ar 7tf+sy,f,8zpvba l :re the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock iz,d16z vrvjt5 /pq6ipnto a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to ac1 6 z5dr/vptv6z piq,jhieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater-drso8x 2-e tl’s body as a solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly agaie8ts l r-2od-xnst her body.   

  You are designing a clutch assembly which consists of two cylindrical plates, ,9d.+xau i7ks 3 klrrcof +u37i, sra.9k kcxldrmass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r)u2es-x1.o rvrtedm/ q(puvzx ;1 l8c rolls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it mezecxl;1s /vq8r.u2 px1 u(t vdr-)ois to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not asgd9)dl3vjr21cg8 dvh vr+ pn:b kw9 5rsume $r\ll R$ h =    (R-r)

  The tires of a car make 85 k ivj)8 3hngj3dc5h edi:-y,srevolutions as the car reduces its speed uniformly from 90km/h to 60s 3jh d8 jiv,3gh5)i dc-kny:ekm/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s