A bicycle odometer (which measures distance traveled) is attached near the whi c/ nz7*d5ca, d 44zgtiyqj6heel hub and is designed for 27-inch wheels. What happensa c/g*t5ic ndj6 hd7q zyz4,4i if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a ptd7hngkl0( a 7jn,cuv;p3 3vyoint on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have3va;l ,nnhtpd g3c0 uv7(jy7k radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described 3 d9zbeg c4dg):ko+ s+ rmpef,by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater t y3srjcxr 25(rorque than a 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 than ws6flwl+ vyut 3b+a/ w/hen your arms are stretched out in front of y/u w3 /llfs6bwvayt++ ou? A diagram may help you to answer this.

A 21-speed bicycle has s y kigqhl620w7hctsf(x- y/ r5even sprockets at the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket?i g6x hf-7kqhlc/y05r 2tyw(s Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on0z vktu 7;,ub*+cs.tuv, ldkl being able to run fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rous.k,cdv* lkt, ;+bvul 7t0zu tational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a l9 u6 8ovi2 bj7)2gpxdquxgsd: ong, narrow beam?

If the net force on a system is zero, fs ei-e0;pp 4ryt9or1(o+f qqis the net torque also zero? If the net torque on a system 1e + qesopr9 t-i;rf0 oypfq(4is zero, is the net force zero?

Two inclines have the same hei4e n 5ttg/p-twght but make different angles with the horizontal. The same steel bt-etwn5 g/t p4all 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 rolling (from rest) down an incline. O.vr hbrk ex6,h:oxu9 3ne sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater 9xx:3vk 6erbuo, r.hh speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder havnwya5 (p69l ije 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 spee j65p9nawyl(i d at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum-ve3euzp+rr um; is+o8-bn2 z are conserved. Yet most moving or rotatiip z -uenubzv2e rors ;m-8+3+ng objects eventually slow down and stop. Explain.

If there were a great migration of people towarzdg7:i nq.m yhbfju lnz0 m 46f(si+:7d the Earth’s equator, how would this affect the fdy4jm7sn6i7 :l.z hmuq gzfi0b:(n+length of the day?

Can the diver of Fig. 8–29 do a somz2 gx6cdzii4j1t9/ fkersault without having any initial rotation w 2 gjz46dif1cxtki /9zhen she leaves the board?

The moment of inertia of a rotating solid disk about hax9;dy+ 0dw* gemix5 an axis through its center o0x a*+xg;5d9yh emi dwf mass 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 mass in each ou, r8s3lv7hvwji*3j j utstretched h3r8jl, hw7s3 *ijuvvjand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical ,al+rqk* n7qusmxwb l z706d .and have the same mass. However, one is hollow and the other is solid. Describe an exper n76 z*dm0lrxa 7k.+ wls,uqqbiment to determine which is which.

The angular velocity of a wheel rotating on a lrco*w bf4rv4a px1,*horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linearl, rv1rx4*4bpwaco*f 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 rotating tu9 : y(p(mcznigrntable. What happens if you walk town(cp:iz(mg 9 yard the center?

A shortstop may leap into the air to ;a*art:9u mip6;:yg,d qsx fb catch a ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite 6 fam,::*x gtuq;;s ar9bpydidirection (Fig. 8–36). Explain.

On the basis of the law of cons hkq zza.z6v9q 2b*agfwqc0-9ervation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the hez.q-*c6fqhzkq 0 a abgv99zw2licopter stable.

  Express the following angles in rad)2gksfe yn9eip r4+b4 sv+ w/tians: (a) 30 $^{\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. Calculate, usingduq6k e-uku 5etu-x :( the information inside the Front Cover, the angular diameters (in radians) of the ( dx5kue ku-eu:u6-q tSun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Ear*. 3r l ngd)b siehhg+u50;kxyth. The beam diverges at an ane hr+)0k sn;xi.yghg bl*ud5 3gle $\theta$ (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 r xpv-v-;+kq bupm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slb-+upx qvk; v-ow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If t:xhv 2,- rqty- vrf6qthe ball makes 15.0 revolutions, wha2-q v,v th6rt-fxryq :t is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How manyryco6)biu -niz2k1r0 )p) erk revolutions do the wheels make pc 2-1eib)kyrrr6)o inz0u )k?    $rev$

  (a) A grinding wheel 0.35 m in diameter rgw545yfkmflshd4p1m x u l)2)-k.rv hotates at 2500 rpm. Calculate its angular velociudmy fl245)wk lv5s 1g -.x)hrhmp4kf ty 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 s (Fig. 8- ) u(7,rcg:s qxohvim–38). (a) What is the hu- risx,v g7:qm(o) clinear speed of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velo1i;)y.a qfuy6 l- rdgc);qbcbcity of the Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a po -ii6 hg0egeii0z1ji916sgwiint
(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 partictjn*xj7 ll f.gg)2p:hm4ow:nle 7.0 cm from the axis of rotation is to experilp hg7t.::)2m jxlgwf o4 j*nnence an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly abou+cbh k7 wi)1xdn-epecusc6:zr8r2a 8t its center from 130 rpm to 280 rpm in arzs7:e1ned r28pub ciw8c+c hx )6k-4.0 s. Determine
(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 radiu 44s z)xmgu7ujf4v)f; cb)jjps $R_1$ 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 themkq o0,x3cmly4t x ,r1bselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can 0r3kql4,,1tyc mxb oxbe 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 res,ocl + qi sbi.ptm876yt to 15,000 rpm in 220 s. Through how many revolutions did it turn in thy6o7,.iml psic q8tb +is time?    $rev$

  An automobile engine slows down from 4500 2y gjhrkc3;k w1.3lxv rpm to 1200 rpm in 2.5 s. 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 in a whirling “hu;xdbrbi/pq w(j +k-vk 3mz56v man centrifuge,” which365 dk;xqvbm ji+ /rv-zbw(pk takes 1.0 min to turn through 20 complete 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 accelerarfoi+af/-l(3hsl ;j2g nw je 29lkpi1tes 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 this time?l 3 pi (1n+his;j o/l2j2a9 rgekw-ffl    m

  A cooling fan is turned off when it is running at 850rev/min It turnk ( bx35aru plbps-;tm-57owxs 1500 revol7p u sxxo-5 5;rw-lmabpt3b(kutions before it comes to 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 unifoll. bj f( zq0n0yu6d4lrmly from 95km/h to 45km/h The tires have a diameter of .dblly0u4n0 6(q fljz 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 th1q5ak9a+rdt k e car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.801r+k5k9tq a da 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 her weight on eachav/ 60) p 6wvsn)mgprl pedal when climbing a hill. The pedals rotate in a circle of rnv 6 rl am)/gvps60wp)adius 17 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 bax x+5y.qss+ 55 N on the end of a door 74 cm wide. What is the magnitude of the torque if the forsbqs.y+x5ax +ce 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 i 7 xayj 5qrmr 8,9;r+3ooxbswgn Fig. 8–39. Assume that a friction torque of 0r83sxywg jmro qa, ;o7+ br5x9.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached j. q vzaws*/1hsv5t )vto 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 released. Calculate the magnitude and direction of the net torquezvsq.v v*j1w h s)at/5 on this system.

  The bolts on the cylinder head of an engine require tightening torc pd*bgdi2e nwkds4*9j0 (d ( a torque of 38 pnw b24g(djd0s cer*9(idk *d$m \cdot N$ 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 r (c,)xauq i4oec8tqbt,ux4 9 uaz y5r0adius 0.648 m when the axis of rotation ,a qab84tt4r yz5)eqxi,9o ccuu(u0x is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bt, 214lulpbpp/ nr7zgc3v1tgicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.21g/, pv zr7b 1gutlp 4tpn2cl35 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 eue crv;x)313lng.ux a horizontal circle of radius 1.2g.)e;lu3 3e1xr c unxv 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 wh bao;i7(2e p n,7rjxraqwss47 eel rotating at constant angular speed (Fig. 8–42)a(2 s 4 77o sjbx;anw7rrpei,q. The friction 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 inertia of the array 4(pxq9g0pj .do-7s ys 2bodozof point objects shown in Fig. 8–439 7-o2d0xo ysqb(4 p .pdjzsgo about
(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 whose total9d;bm0fg (hjl+rugj 9) upb. p 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 spinning at the correct rate, fq/4;u9m ixsk engineers fire four tangential rockets as shown in Fig. 8–44. If th4ufs/k xm;9iq e satellite 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 msd.z: h;at 7u h8jap+ xiu/3esq*s/nand a mass of 0.580 kg. Cas/sp 8t7.*ns hx qah dzu/ue+;m3 aij:lculate
(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, accelerating it from rest e8ph. 4a)qyo ktil3 q1to 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 smzq/fl r,-v3yqkia )xq* ppl76all hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rp,qk -qlrp6p lai37)xf */q yzvm in 10.0 s. Assume the merry-go-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 rp39w5h6ki b: mn9uheju m is shut off and is eventually brought uniformly to rbue wj63k i5hnmhu99 :est 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 ball :ya eptn;v1;2hw :gvgat 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 bk-qoqtfmve.ijpmx)1 7(zd ja:u 5 4s/all is thrown solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps musclzaukp 7mf/54j-sqxi :j). dmtv (1eq oe, Fig. 8–45. The ball is accelerated uniformly from 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 can be considered a long thinlidr c. 40c4mk1jfex1 v)q6vq rod, as shown in Fig. 8–46. m.0vk416vdr 1qlf)ijqxc c4e
(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 masses,kj(o/g qcv+j x853rr pv8s1uu $m_1$ 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 four full turns -z eemmt 6ah0ect05l m*. iw,m(revolutionm0li.a m tce,mmh*5tez-6 e w0s) and releases 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 momwey1c6s .)w pdent of inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops aq,yod jzl (h1, torque 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 9d ;j gk--wf n 5n.)yj8fwvpyi.r1v lp6.0 cm rolls without slipping down a lane at 3.3nfn1vyfvy-85)p6.pgjk .w dj i;- w lr $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respectog9re dyo bp-oc*6/.o to the Sun as the sum of two terms yo/ db9*.p6-o ogocer,
(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 of 7.5+k uejw5j9d p)0 m. How much net work is required to accelerate it from rest to a rotation rate of jkw9ep+5 udj )1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kv u8gniz 5 ams1cnrt2ag;2+ n)g starts from rest and rolls without slipping down a 30.8nzg5autr2sa v)g1mn+;i n 2 c0 $^{\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 balanced vertically on cde:7q7za(7 ss(j bdr7+ mdx dits tip. It starts to fall and its lower end does not slip. What willq77sdsb(dd j(x mec7ard 7+z: be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the end of a 9u-h4 +bn:rebba)acy7bp nv:thin string in a circle of radius 1.10 m at an ar : c9ye:4h-)a+7bubnbv pba nngular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular vr iro5opa3,0f8g5g kmomentum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm 5r0gagk irp8o,3 ovf 5when 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 at a rateq4e1 ub :*:sq2 cd v29pulsfar of 1.3rev/s If he rais2peu a*rdq:cu9s1b24sl vq :fes his arms to a horizontal position, Fig. 8–48, the speed of 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 tb2l06. zgvuz/ed6km ) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5zg /60ukzlt6e.2mv db 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/+zskp.y d;q h,mgcw+ initial rate of 1.0 rev every 2.0 s to a f,/zwqm hd+. pk;cy sg+inal 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 rotating around a vertical axis through its 66*fymv7t ab.no ih6 4g/kpzrcenter at a frequency of 1.5rev/s The wheel ao ngi7h tyb6z6pf*4v6./rk mcan be considered 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 osj-5 bqiocjm e0).-1sdss:: tkc0 nac f a figure skater 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 mo4.rhoy n-*i ttmentum of the Earth
(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 a9( ticfkyo- )dropped onto an identical disk(oif9 -c)a ytk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns 4j5b-/ bn co zgj2uf)g*de) lbat 2.4 $rev/s$ 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 stands at the center of a rotating merry-go-round plny0jwq8i :ygj s8cgdu+g1e5/b z ,n)f atform of radius 3.0 m and momentbg1j in gq0y,8cyn+:g 5)jz df8wes/ u 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 is rotating fre2mtxh 7doduwh3,-mu mam8g* :ely with an angular velocity of 0.87mx:uwo*hmth3g-m28d ma , du $rad/s$ 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 eventualp6dh1l s t30hhv pkclt/.q+o: s9yi0we 6 faw3ly collapses into a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing ra6tha /p: e6plhlwwi1.sk3dq c0ts3y90 vhof+dius. 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 winds in excess of j(gc qab x9t:l1s/f:zee-z8e 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 7;d9+q4fkj1zglc s ww$ 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, ths 6)i- sksrmn2ss xyl3 h0gs;7at can rotate freely without gys; -s0l273s sxhmn k6sris)friction. The moment of inertia of the 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 stands at the edge of a *v xi0,o/ fq3tcc.l zk6.5-m diameter merry-go-round turntable that is mlfc3.ciz0, *qtok xv/ ounted on frictionless bearings and has a moment of inertia 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 wit 8- d3hq1a.uw(yiiftnh the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behwuhad8fyi .i n3( q1-tind 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 tc 2chgm)vf u4hkokkz2g:o, h((vf 2a2he same side always faces 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 the Mo4gah2h( )kvku,ok f(gvc2cm2zoh :f 2on as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of .a/ fl+n+diq z1 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 in +t ) 2zzd*yg3 0kqn/me poe0vathe shape of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant emp veq )3ynz+gk/ tadz02 *0oangular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of ma v-;,(v ;yfjd 3fyqetgss 0.050 kg and diame3,fd-gjvtvef q(;;yy ter 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 string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the rea0*sm dp)qt(l3y u3 r3e0ns tt(oujj(k r 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 ows j7:ud-r. twf our Sun, but 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 collapse to a neutro rj.d7wuw-:tsn 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 automoj5 yd+4.vyyiq bile is for 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 ayqi+vy y5d4. jnd mass 240 kg, and should be able to travel 350 km without 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 illustrates an os1 a8gw1welv vjz 0.2$H_2O$ 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 rollin+1m- k-p yf n;lzmel5kg on a horizontal surface at speed v=3.3 $m/s$ 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.,yd;:( hyyr p*szp/ 0ee 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 of the rod, and (b) the linear acceleration of the tip of the rod. Assume tha/d yhy:;se*p r0e(zpyt 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 standing vertically on the 0w) s.az21ep e0qqjwryuta27floor, and we want to exert a horizontal force F at its axle so that it will climb a step aj0e rtqw)p y.a 2a1ws 07q2euzgainst which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on awm -jg5y0)7: po0n osc0hl et4kx0tma flat road is making a turn with a radius The forces acting on the cyclist and cycle are-4hne 0 k:pcs t75 y0lomg0j)xtoma0w 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 into a +j aj;-pao9aw 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 achieve+jpoa- 9jawa; this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thin rods, ma(; bdlqh8n bev m;o6+cking reasonable estimates for the dcb(hbe+;6 8nql;mo dv imensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylin e ;u-mnaclt 4(u-wol3drical plates, of massmu3 ntca;w4e l--u(ol $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 rolls along the looped rough tr3qzs, ,ci,tuz ack of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest po i u3qcs,zz,t,int of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not ass3 x*j/md ,pc,ixine5dume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the cax x5/p c;-+p 7*fedde+s,rql2kst bvtr reduces its speed uniformly from 90km/h to 60km/h The tires have ;k7xdb* 2f/ e qtcx+tdp rv-e+s5pl s,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