A bicycle odometer (which measures distance tr c8-f ru7 .51w8ifmi s vnzw.3xdlsbe1aveled) is attached near the wheel hub and is d.fus -x8ir8.3 wms571e zd inlb cwv1fesigned for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point 0jl v g3ciar44on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have rad0aj c43lrvgi 4ial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body :; cn/tr-z6 shei-pyuqc0sh-4l-vk j be described by a single value of the angular velocity $\omega$ Explain.

Can a small force ever ex)9cvc5j a+ xi1xdw m2bert a greater torque 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 ( lb,lk:v/pnj ulf pyxq/2 r*.to do a sit-up with your hands behind your head than when your arms are stretched out in front of you? A diagxuy: pnlqjllpkb2, / *.(r/vfram may help you to answer this.

A 21-speed bicycle has sevenxh4ih9v9a11k k.to.m s bw6v il7w(nv 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 sl 1.nh6ka7voh(b kv9wimw xvs419 i. tprocket? 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 fm.jd +5wll n58-hevvyast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why jd+ny5.vhwl 5vle- 8mthis distribution of mass is advantageous.

Why do tightrope walkers6lfcs-+sz z2 n (Fig. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net torque alsox6 h+ *hr s:pvka0 r(b8u4wt8t g6sasq zero? If the net torque tgv h s4sha6suxr(:8+ 60ktq* parbw8on a system is zero, is the net force zero?

Two inclines have the same height but make different angles woj;f cb0o6/jw ith the horizontal. The same steel ball is rolled down each incline. On whichj60ofjbo c;w/ incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously star*e6hbf8a1 yaemic; 7pt 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? ab 7yf6p;8 m ech1ea*iWhich has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They r8q pzvr m(:k(6(eo1 nm-ighostart from rest r:zkgm1in ((qp(orm 6 o8v-eh at the top of an incline. Which reaches 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 conslts7i w cc2l37erved. Yet most moving or rotating objects eventually slow down and lil3 wc7t27sc stop. Explain.

If there were a great mf : 7*nqsk q2p+qtr+ukf4j5wfm uo9ya,1 vqq6igration of people toward the Earth’s equator, how would this affect q o1*mqvt4 j:ukaqwr fn +2fpsykq u796 ,+qf5the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any inie wqpn/q1t(zz (twoq (xy :70ztial rotation when she leaves the bo1qw0qxoq wz:(e ( 7ny/ t(zzptard?

The moment of inertia of a rotating solid disk about an axis thr4zw fyx9hytqy 6+g9r1ough its center of m4 r+ q1xyzyghw9 y6f9tass 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 outq(xggq;j3i -a stretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, i-g( ; 3qjgxaqor stay the same? Explain.

Two spheres look identical and have the same mass. Howevebpas tg, z12adgp1va 7dq4h 64r, one is hollow and the other is solid. Describe an experiment topq6a,dp7 v s1a zba2gt1 gdh44 determine which is which.

The angular velocity of a wheel rotating on a horizontal axle 2bv7.kmt+ lbp2y 9*xb*chvbp 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 linear acceleration of this p b.byk2chm+ *b *9pxv7tbv2ploint 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 turn-ur0m:1 wt999q(r ythccqbeotable. What happens if you walk toward the centere9b0 r1hw cqu-9o9: m(yctr tq?

A shortstop may leap into yl1tc2na12z bx0-(t*prvxp b the air to 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 oppos0tzxbnpb -ty(r 2*c1 2v1palxite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular mbt0s2b8 9 lsur n*ll-komentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the kss ubll *8br0-l9 t2nsecond propeller can operate to keep the helicopter stable.

  Express the following angm, i.e7bl1i reles in radians: (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 coincidem7 dm:4s/fbss2wp*faf mo3w4nce. Calculate, using the information inside the Front Cover, the angular diametersm fasd*owpf 3/b7ss4f4m:wm2 (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moo,glu ff9(, q;tiuem*lx q/my3n, 380,000 km from Earth. The beam diverges at an anu,/x(mm lq;gi3t9 qey ,*lfu fgle $\theta$ (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 ttdnn7 3yn 9x(o(m; fy s62lqzjhe motor is turned off during operation, thm;n9f(o7t n6zyyx q(d s 32lnje blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to anddyk+,*6pr qxozb, q6to / xo;other child. If the ball makes 15.0 revolutions, what is its diakq6t ,odb/xyxzpd +o ;o,*6rqmeter?    m

  A bicycle with tires 68 cm in diameti+ d s(t/oh0bvf pfh/ .r4*pr:l0,ux g8epnp mer travels 8.0 km. How many revolutions do the wheels pm8igv0e,s 0bpu(rot r fn:.ld pfh4x/+p h */make?    $rev$

  (a) A grinding wheel 0.35 m in diametw ,hjg-2 d3h-licxo5+qgz j5ser rotates at 2500 rpm. Calculate its angular velocithxsqgw2+gi z-h5c jo5j, d-3ly 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. 8–38ql t)hhe kz*)*). (a) What is the linear speed of a child seated 1.2 m from the centez* h))*eql tkhr?    $m/s$
(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 e:g/y)q giq8rao;)f paround the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed ofr 4mtlp93mb v2 a 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 :hduksa8un zf-4 dxt)i1.1r pcentrifuge rotate if a particle 7.0 cm from the axis of rotation is to experience an 8x 1fku.)p uah1nzd srdt:- 4iacceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerpo (ov2)pnp1nd4ccl /ates uniformly about its center from 130 rpm to 280 rpm in /v 21onp4dc)(po clnp 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 radius gm3;ot: 4iyea$R_1$ 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 spacecraffk s71vo oz34rt 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 cylinder oksv34 z7rf1o 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 inisi *o8/w8 boccw37u l 220 s. Through how many rev iol/owwbu8 cis 378c*olutions did it turn in this time?    $rev$

  An automobile engine slows down from 45056jlo 2cxdp 5a(vf7ke 0 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 dwpu:q/y mw7 9stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min tq/97 pww:udy mo 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 acco w()df6bq duejyl0f;.m2t 5v( kd2u oelerates 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?6odoe f d.)d2mw(vuu l 50;y bft(2jqk    m

  A cooling fan is turned off when it is running at 850rev/min It turns 15ypto( *xjjw2z o5o q)000 revolutions before itq t)j*(5 ow0yj2oo pxz 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 revo 1/noq:erzxz ;l3 :;-gnvr ijmlutions as the car reduces its speed uniformly fro ;g inr:jl:r1v; e zonmzxq/-3m 95km/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 as theibk e zv.b4w7tang09mm v6h 3* car reduces its speed uniformly from 95km/h to 45km/h The tires hbnawzteh0b v6k .43 g79im*mvave 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 b*nx cg:6c qag9ike puts all her weight on each pedal when climbing a hill. The pedals ro6g*:anqg x 9cctate 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 of 55 N on the bkspkl ;5 hfmn0pw:stsi3hdb5v2 ;+9end of a door 74 cm wide. What is the magnitude of the t0iwsfh95dhbs;t k p;:+3vnplb 2s k m5orque 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. 8–39.2 )09ogh;ihcmzf.8xlqsw:iv Assume that a hzi h92 f ;cxvi8.qswo:lm0g)friction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are x9hk2hlnjd69attached 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. 9njh2xk9 hld6Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engin8we(dz+ dun9qe require tightening to a torque of 38 nd w ue+q98d(z$m \cdot N$ 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 0.648 m when th n.z uj+ln.hf5v9v3 afe axis of rotatiof h +v3z9nla uj5v.fn.n is through its center.    $kg \cdot m^2$

  Calculate the moment of iek.xvwp6 4d :nnertia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can beep6vdx.k :4w n ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotav0 /e2xi9 r7a2g3d iggopbky0ted in a horizontal circle of radiu9 i2gvp g 0xre o23bg0dya/i7ks 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 c9w.a 3if;ayr2 ipa4z bowl on a potter’s wheel rotating at constant angular speed (Fig. 8–42).r.ayczwa2 f394;i ai p 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 of point objects shown in Fig. 4m35 9bau s1d2bxawef /6totv8–43 abou v1b9bdxa / 4u2s3m5aofetw t6t
(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 mass isk*34qpr , m(vdi*jki(l kmj e4od:y4s $5.3 \times10^{ -26}$ 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 cylimu y+3 .nfvhzp6 b36qwk6bt.gndrical satellite spinning at the correct rate, engineers fire four tangential rockets as shown in 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 5n3p q tbg. v6wfh+36ybku6zm. .0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylin6 r;rhh3uf++uk 0 ltqnder with a radius of 8.50 cm and a mass of 0.580 kg. Ckr ;f u+t3hu h+60rlnqalculate
(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 fromh9v5w oktne- ,5+jgx 7 zpa+kp 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*/74fm zm1icnqgoj p, -driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm 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) sitmz 7,1jp/iocgm4q f*n 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 n ei9wxgavr drv2kag; 1) g4+.rpm is shut off and is eventually brought uniformly to rest by a frictional torque of 1.2ie14;k rwx)rvdn .gaa 9ggv+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 3ve4+a+ 6odgnh.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 the action of thm ji; kf q.s;y.kbco88e forearm, which rotates about the elbow joint under the action of the triceps musc . skbci8qk;;jyom8.f le, 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 bl5mqlxx4cbw b0 -he86v znp04gade can be considered a long thin rod, as shown in Fig. 8–4ezl x-v xg8q5np 64b0hb c4m0w6.
(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 jeono1(on:k(k(/)uk, ulx dzgwf09f masses, $m_1$ 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 turi3gefi ,56 lfxns (revolutions) and releases it at a speed o lf3,i56gx efif 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 ovm d oh58y(l*drg *kjhf(o-6 bf $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine dlzb,hb(r h; -develops a 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 9.0 cm rolls without slipping down ab1ftp .:cy d5c lane at 3.3 .:f 15pydctcb$m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as therxsv)*g-kgq,gc ,bj 2 sum of two tev* qb csg-x ggkr,)2j,rms,
(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 hass h ,iw8i2e09ywtxe:u a0j fc+ a mass of 1640 kg and a radius of 7.50 m. How much net work is required to accelerate itt0hu ec, j yae0six92:+i fw8w from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.8mk6a cqd/ x7 d8sx4m53krb7uv0 kg starts from rest and rolls without sl3/ cb6q5d dksv47ux8ma mx7 rkipping down 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 itepkj v n429c w0be ph;2zpw+f*s 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 grou 9ke2;2fw j4p b0n *wvppehz+cnd? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kau x jjvha22 q4wz(y30g ball rotating on the end of a thin string in a ci2uq(yzva hawj j0x4 32rcle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momen s9nqs2s4wox floq: g)y da(yu0n *(7gtum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm :s29 o0yx yo(g(nuas*4 qd7fn)gqwls when 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 rota1zpy)6utrg (tu6 rkqvod)j2 6ting at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decrea qu2 up6 v6 trt16kdjgo(z)yr)ses 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) can reduce hrl3 qfmi7n 41oer 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 when in the tuck position, whar 7lq4fn mio13t is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate fropl d v01,gdgp9xkx n,;53opjvm an initial rate of 1.0 rev every 2.0 s to a fina910djdpg3ov,x pkv ,lnx5g; p l 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 cen)wjl5qx 2)njwter 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, onto the center of txj2l5wq)wj) nhe 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 figu5ho11 x;jiyuhw0d (hlre 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 mofpm j.k,,qd.j pvwf;un)6 zn/ mentum 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 inertiamq5f-n bo2lx/);rdw a I is dropped onto an identical disk rotating at angbq md/fwar ;)2l-ox n5ular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns ampb 5nxf -r ,nyipllh8l3yr71c /(: tmt 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 pla ts*qnwd7p1o k6t*5 lktform of radius 3.0 m and moment of i6tkd1 wk5p * nt*solq7nertia 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 freel8sno-1heh rc9y with an angular velocity of 0.8nhc r -o98s1eh $rad/s$ 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 in wi/2fp)k -vzfoj5le9 to a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. 9/e-k25pi)lf wvfzo j 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 involdtw 1lyx hhy7.z9n8,r ve winds 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 sq wp*k+z)og3$ 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, that can rotate fr lh 6e.nu- x4bhgdt u0,ob0 jk25dd0 emgj*sv)eely without friction. The moment of inertia of the person plus the platform 05 x gs4 j - ge.lhjuu dehbnbm)0v2ko6,td0d*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 6.5-m diameter merry-go-roktdr( ic1qy0b /nk(.tvm1j f2und turntdnf0/r2k .cqtvmj (1kt 1(ybiable that is mounted 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 o4flxni jtwx:* 9x 6z+on the ground with 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 behind the person without xwo l9: fznxt4ij+6 *xslipping. 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 faces the Earth. De2 w7-yvygylv)47c/lrwd ghl*termine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital anguy-7gclrywd7v)v wg 42h/l yl* lar momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of 1 m/rhs n1/7suun0tps d+/ e);m qpq5xp2o$s^2$ 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(l 3h+k)vntrr the shape of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s intr t)h3+v n(rklerval 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 0.05/)bc rdq :9m bv:nprf: 9o/kvq0 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 liner r d9bc b/)fpm9/:k :vqonqv:ar 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 5ks33(;opklvn lw(8 -mgg zj athe angular 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, but with mp);x4h2k gngs ass 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 that4g nh)gk2x; ps the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobilcxcrt wln1 h04)r. f-rs:k8shq (q(jf e 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 hrcl (qh1sw4k cjf).(rx0 r:fn8t-qsof 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 illustratu ccol4),ep+x es 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 eol8cn 5qs8hq00w tl :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 an0+trgjngv4p8 r je9r; d length L can pivot 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, dg9jer;8v+jn g pr4r 0tetermine (a) the angular acceleration of 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 rad)0to r5bg1 - vb(wgzh+kfq dq5ius R. It is standing vertically on the floor, and we want to exert a horiwtogbb(q5grz1v-kh + q5) d0fzontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with s ez;icjye: 1ghy4w/ 5wpeed v=4.2m/s on a flat road is making a turn with a radius The forces acting on the cycliseey4wjz:y cw;h 1i/g5 t and cycle are 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 sling of length; /6*zf +uuc kh iq0yd9/qm3ikt+lcuk 1.5 m and begins whirling the rock in a nearly horizontal circle aboveihc/qi q+kyk t93lzduumkuf* ;0+c6 / his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What 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 rods, migawf 1m3 /ou.aking reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched w3og/if1um .aarms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindyuf -9z+p i/qw(vn 8uwrical plates, of massqy9 p+/uf vnzi-w wu8( $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 alydc7i0ch 65d hong the looped rough track of Fig. 8–58. What is the minimum value of the vertical0 7i6chyh5d cd height h that the marble must drop if it is 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 asv9 ikh*4zfvy3sume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutim lq09-e5os8a kde3 qeons as the car reduces its speed uniformly froq3kee 9-o0ad eqml8s5m 90km/h to 60km/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