A bicycle odometer (which measures distance traveled) is ate-. c 8tw cr r3gn)ub ;ovsb(ryc70-sntached near the wheel hub and is designed for 27-inch wheels. What happensso-b v(nn s;rt brc8w-3cuc) 7 gey.r0 if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at /qpo e4rcmz3a s 7z4 4)fpb:wsconstant angular velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitudw/ fqasrpe434) c 7bzpzo4s:me of either component of linear acceleration change?

Could a nonrigid body be described by a single val h v5,fowm),fnue of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? 1qbdh v+yorb x150x)dzx8jw(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 be) m4ekk:p(qyxl,w0ua c ,) iqhhind your head than when your arms are str)qh,lxuk, 4wqc) pi0e :( mykaetched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at tqon g(g2fy 8ub2bup x+w5a*n) id65d xhe pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprockeb 5d ognfwx8)gbd*5 iun2+x26yuq(apt? 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 lower legs with fleo1s;e* *axj: )mi8ip lgt *vkosh and muscle concentrated him*k8jv) :glt**ao1ioixep ; sgh, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, na y1a3,jd b ,k:xwmf(nyrrow beam?

If the net force on a system is zero, is the net torque also zero? If the net to(eat, (:1jp( qztrt jq.ejm8irque ojr.1 p:ejti(at(8(qtmz ,jq e n a system is zero, is the net force zero?

Two inclines have the same height but make different angles witv 4e5nkq1de. hfdf:.wh the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater5wff:e .e4k1nvh.qd d? Explain.

Two solid spheres simtv) x-jws-,qm; ilrai)3c6ryultaneously start rolling (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? wmx-ar,r6vs)3l;i qy )j-it cWhich has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They +5xktt /6s /gnf-cyf lstart from rest at the top of an incline. Which rea5xl+t ytgc f//-fn ks6ches the bottom first? Which has the greater speed 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 are conserved. Ye 28td+t7sbf)tdqh 0qw t most moving or rotating objects eventuallyqq+bft td0 2swh )87td slow down and stop. Explain.

If there were a great migration of peop pyi4yyl+0d, rle toward the Earth’s equator, how would this affect the leng 4ldrpy+,yy0ith of the day?

Can the diver of Fig. 8–29 do a somersault without having any initial la(/mqlt nr40 1madi*l;gh 4j rotation when she leaves the ndi/044lmh1r(a j;q m*alt glboard?

The moment of inertia ofh9 kct-.7cwzd0xj0yz a rotating solid disk about an axis through its center of massxzwd9jt0z0k7y- cch . 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 tb q/+j)0s9 vpqat9ill/q qr 4on a rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, 09v //sqq)+tt9ilrqjlpa bq 4will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical an5(atiw i; jp3kd have the same mass. However, one is hollow and the other is solid. Despiw;3i (5tk jacribe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle points west. +g pnpeb-j ;vbd4o2 :xIn what directio- p24pj+xdn:;evbo g bn is the linear velocity of a point on the top of the wheel? If the angular acceleration points 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 on8fqdjqeo ,dlj)u1;g j ki(/g.py/ml ( the edge of a large freely rotating turntable. What happens if you walk toward l/i ko,j8qjd(epd ;lg .g(u)q/yjm1f the center?

A shortstop may leap into the air to catch ) 5ji :)cnjxo8m n41d wsv0mam2o.kwqa ball and throw it quickly. As he throws the ball, the upper part of his body ro1miw.)0aoc:q) mndk8 jm 524s vwonjxtates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of cons6xto ::l:lbpcs / . cnn+gh*ewervation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propel:n*s gw.lbxce+oc/ nt6:: plhler can operate to keep the helicopter stable.

  Express the following angles in radiw vmgwd8c (9h;ans: (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 Enramdvy)(fi395 a4iv arth because of an amazing coincidence. Calculate, using the information inside the Front Cover, the yi43ivvm nr5fa)d a(9 angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km fie 2t((w umuh0ppvx 30rom Earth. The beam diverges at an h u(0 0wxum(it3ppve2angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blende 8fm0nopo ajpdf9l.) 5r rotate at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the.d90 pj5om)n la8of pf angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to anothern-9gz(a i-h rn0oiuv2 ,dg/l d child. If the ball makes 15.0 revolutions,g,(-i/avhr9 o-02d ngilundz what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolut z lof:y j9in.sg(ru/2ions do the wheels s g n:29urzj.yilo/ (fmake?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at + 4kz)nf78j/9gvdigf fn q4j q2500 rpm. Calculate its angular g4 9v/jdiqn84jz qk )fgf7+nfvelocity 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 mai2whj*2,yy y) k:2kwq;myqiskes one complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m from the :h)q2,2qsij kyk;wymyi2y w* 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)yvwu6 zo927e u 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 poinw o-zl1v,te .pt
(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 centrifug 1gtqy *4)s.b+yda -hoco1h rs6nf-h le rotate if a particle 7.0 cm from the axis of rony6ho*+al-1qs tyd- rbso) 4fh chg 1.tation is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about jy98kux km7if5 2got 1its center from 130 rpm to 280 rpm in 4.0kxug958kfj7my o t 12i 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 radius0gp7x-xdy a,i dia6 m. $R_1$ 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, asts2n 5h, ybzeel70lxx(ronauts aboard the Apollo spacecraft put themselves 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 be thought of as a cy,lx75h yn20eles zx( blinder 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 r3pw g. bxz:y)vest to 15,000 rpm in 220 s. Through how mav)zw.g y3b :pxny revolutions did it turn in this time?    $rev$

  An automobile engine slows dcst/8snr 71g-si, 8 qqhfqbs -own from 4500 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 stressedg7ptty4g9 y3ln0o/k s of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions be4t7do9gk/yptln yg 30 fore 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 accelerates uniformly from 240 rpm to 360 r gqi p hb iogvcg ;s63::ek:x94)asf,fpm in 6.5 s. How far will a point on the edge of the wheel have travele)vfciqk4, shp:gag 3o :xbif: e9;sg6d in this time?    m

  A cooling fan is turned o e1v20x s 0ecju8-kjbzff when it is running at 850rev/min It turns 1500 revolutions before it comes to a stop- s 1ue 8jzb0e0kvcx2j.
(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 pobsmt2e3e 2z,xd0t1 vb4ch r q,71qxreduces its speed uniformly from 95km2qzv,ht te1,bc30rop xqm2 e1s bxd74 /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

  The tires of a car make 65 revolutions a9 w7jbv.sj ro0s the car reduces its speed uniformly from 95km/h to 45km/h The .wsr9o jv07 jbtires 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 her weight on each pedal when climbin9pa1mu9syx.8 8j zkn1ta:qj fg a hill.zs8j9a fk9pujtm 1a y8x:.1 qn The pedals rotate in a circle of radius 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 / h )h6mrx9 qux6of;lyf) nnln0x0fn7of 55 N on the end of a door 74 cm wide. What is the magnitude of the toh6f 90l)xr0on xhq nn)un 7x/fm l;y6frque 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 abjuzsqmfz xd)s-9t *)9out the axle of the wheel shown in Fig. 8–39. Assume that a friction torque of 0.ux) q d9ztz-s9*sfmj)4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, a zc*l++1iv vtare 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 released. Calculate the magnitude and direction of the net torque on thisil+ va*t1+czv system.

  The bolts on the cylinder zaff+vw l, :p)head of an engine require tightening to a torque of 38 z)lfp+, w vf:a$m \cdot N$ 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 radius 0.64gb q +o8f6/s 3x2yzt9naty:onve: 5uz.a 0gr n8 m when the axis n nt6o/:ogrsfv u5: zyx8tb+ gze9n2aya.30q of rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. The ri+ui 1-u/ 9 v9uawkcadym and tire have a combined mass of 1.25 kg. The mass of t1+uau -9 dwik/yucv9ahe hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end ofcotvq472rq+w)88k p s- dwbpr a thin, light rod is rotated in a horizontal circle of radb24r8 pwvo+q7-cptd q8 )w skrius 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 rotating8jfm 8aftryun t(71e: at constant angular speed (Fig. 8–42). The friction forceam7f 8r(: 8utytnefj1 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 of point objects shown in Fig. 8xhcnu t f(m7 cvxzf8d8n3u*8-–43 -7c8n8zfc u*nx8vmhf xtd(u3 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 total masu,q zl9fc j8-hs 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 spinnin g*y;s44mc2*ltlwdrrz 4n3f tg at the correct rate, engineers fire four tangential rockets as shown i2c sr4 4t*;fmg r*zlny3dl w4tn Fig. 8–44. If the 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 l v--r.oee9+ml-gcqb72+oceu e c hnk7 2 ts2buniform cylinder with a radius of 8.50 cm and a mass of 0.580 -rokc+u .e-+bev ecth 7l -b 2g72ecqnos2m l9kg. Calculate
(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 from76kt)d6ounjup7l .ri( s (oow 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-round and isu*sear -/ w9ps able to accelerate it from rest to a frequency of 15 rpm 9* sasw e-upr/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 rqh 4edjjc(* :xen/a6(o xn ;*-fkllhh otating at 10,300 rpm is shut off and is eventually brought uniformly to rest by a frictional torque of 1.2 edkj l4 h/x-;q l6x:eofn*anhcj (*(h$m \cdot N$ 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 aj7ghmju, x 5n2hqe-p6ccelerates a 3.6-kg ball 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 thqi(w* i:9f(3(oykh,b xxvl coe action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accel9 :vqbohk(f,l(w c iy *i3xox(erated 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 thin rod, pc0q o;crt:6was shown in Fig. 8–46.p rw0; ocq6ct:
(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 massesej(jfhj4x w6( , $m_1$ 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 accem 1u5khg9x d/wlerates the hammer from rest within four full turns (revolutionw5g9xhd1km u/ s) 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 moment of inertia of ez93mflok s8zh;)/of: pt7h f *to9 ob$3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torqkib9 .f*ii xn )6mza1m)7tzxzue 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 9:(ll p dja,./ gblapaa 4r3ehradius 9.0 cm rolls without slipping down a lane at 3.394hlg jaalap eb,/:apdr3(.l $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with retl5 b;eazpk gq ,z8(z/ukj2;i spect to the Sun as the sum of two terz5kj/azpi(u l g8 kb,;t2 ze;qms,
(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 7.50 m. How much net woauwh ;o*ez b+(rk is required to accelerate it from rest to a rotation rate of 1.00 revolution per ueoz+h a*b ;(w8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.8ncpr7u z*) (li0 kg starts from rest and rolls without slipping doui r 7pn*lzc()wn 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 balanced vertically on its tip. It starn ro/6b 0p:mxxts to fall and its lower end does not slip.ob60 :n/ mxxrp What will 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 ofn -um od4h08en the end of a thin string in a circle of radius 1.f 8mnd-4he 0ou10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg unifoh o)q qq((b7fih n08k :iojas1rm cylindrical grinding wheel of radius 18 cm wheh) f(ibaqs:n 7j(8khio0q q o1n 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 rate o:;bzow3mtf(xc/ d(n jf 1.3rev/s If he raises his arms to a horizontal pz/ojtxb:w( fnd3;( mcosition, 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) cajp5c*inuy1t7 n qat 73haqr6:n 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 1.5 s wca pj5n1in:t3y ht 77u6* qaqrhen 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 rotatiw is*y0y 8er6: e+ryjion rate from an initial rate of 1.0 rev every 2.:j6yi8 0eyie*+ywr sr0 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 rotating around a vertical axis through i3p- z5 mav8xwvo(8baits center at a frequency of 1.5rev/s The wheel can 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, mibw(aoz - 85av3v8 xponto 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 skater spinning6: hsctk 6wu*j 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 Eart xy8bt jc ba6ckm0s9*)h
(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. po 8sj7rfw4zs.crv3 dropped onto an identical disk rotating at angular fs sc3.78jo.vw rr zp4speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at xqrhv5jfoun /;v0 en 2r7 -nf,)ugny22.4 $rev/s$ 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 c9,km3bnlp; nm2 tl zr3enter of a rotating merry-go-round platform of radius 3n;k3tz,nb 3 pr9 2mmll.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 is rotating freely with avnc1)/r;s ;j9ik wrqr n angular velocity of 0.wk sn ;9 q1)jivr;c/rr8 $rad/s$ 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 eventually collapses into a white dwarf, losing abou u*nsko99 wk4 vejc6y5g6toj)t half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming tgvk owc96s jn4*ot5j)ky69uehe 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 57p4l)x ,q o.eklofvx 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 4vhsjupr) o;5pj(3 rf $ 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 platfor(:k6 ji 0pfrfloj/o /hu22xlyy* f;frm, initially at rest, that can rotate freely without friction. The moment of inertia of the person plus the platform fpoj60 yu *2:/xo(l 2 fjir;yfr/khlfis $I_P$ 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 th1tjsya lcu6rmze (l2 .5r/ h5we edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of cyuh 2wlz6j5m/5.a1etrs(r linertia 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 end of the rope lt- mp)3/ gojgnying 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 behind the person without slipping. What length of rope unwinds fr ojpnm)t3 -/ggom the spool? How far does the spool’s center of mass move?

  The Moon orbits the 4aj6gr77 e 9qq1driyeEarth such that the 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 Moon as a particle orbiting the Ear gq9 er6de4 aqj7ryi71th.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rr.x/df3s ( dopate 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 in the shape of a uniform cylinder of radius 0.fnl1g9xo9s yc462ds n 20 m acquires a rotational rate of from rest oo169f 49sngsn dyc2lxver 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, each of mass 0.050 kg and 8p i7efa50xjjdiameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050xj 07 efa85ijp 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 rear wheel nyh+ d6y2 9c vfmt1ondvg3 u46($\omega_R$) 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, but withb4afnb6nc h7rv )h(fd3) xui 8 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 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 offb(c)b6 hh74unrif d) 3v axn8f no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is fon0/.fd9 ktx rva73pg wr it to use energy stored in a heavy rotating flywheel. Sup fpr 0g9dtn3 7a/.wkxvpose 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 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 ank*m2ni75u 9fkq v m/qb $H_2O$ 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 mct y g6ah .uzytmkew06(x+l0js9jq).lcu)7horizontal 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 pi t9d(ej*snx s9x)/r5q * zdjlhvot freely (i.e., 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. Assumx )5dzr tj/9s*el* j(n9qdsxhe 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. It4 3dq6brwj)xs )yy eq o0()ddk is standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a ste)(ys jko60qqry 4wb3 )ded)dxp against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with *k9p*r.1xiicxzo a n(speed v=4.2m/s on a flat road is making a turn with a radius The forces acting on the cyclist and cycle are.r1*o caxxikp9ni(z* 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 lvxu4 - f4* tn0bftdfj5jq)8grock into 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. Whatnx8f f*u- dtq4l0 jjfgv)4t5b is the torque required to achieve 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 r/ .ytcwan60viq w, vsu1n(ou (ods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds 1tno/wuvvu in,.(s (ya60 cq wfor a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of1g 9tnzekc+3jp fr4, b two cylindrical plates, of mass1pg,ntkz4 c r bef39+j $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 thx9 z nge;rac 3kcdsdx8 a-2,6v5y;+eh rv*umge looped rough track 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 g -sm853a cy9udcx;a ;renk2,zd+vxh g6re*v 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 assumc 5:dqv8x:xfx ff/js*4y.led er.z3 ke $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces itscg -::3jwtbp u8gibt5)vd+v t speed uniformly from 90km/h to 60km/h The t bwt:5:+i vj8t3gpbducv g)-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