A bicycle odometer (which m f l,t*uq oz mk*ugu*40yh73xueasures distance traveled) is attached near the wheel hub and *3 gq,uktx 7*04zly fu omuuh*is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotaten 0pkt7ijxt 4 rs28)yes at constant angular velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity incr)yxtj p0irstk 84 en27eases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single va.1k/thbh pz f)x5rd2hlue of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force?/ .t;t+i nxdhixhz6;d 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 wbd8k+0loc0v uuf6ah * ith your hands behind your head than when your arms are stretched out in front of you? A diagram may help you to a8bvd lkhfc0o6+ *uu0answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at the peda k bf 1v5,z;eowo.g1(;p6 lkv8jaz ldtl cranks. In which gear is it harder to pedal, a small rear sprocket or a large re jzkawzo, ( ;6.1tdpe; ovvf1l8gkb5lar sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend onmki1 d.*f ytftnx fy,s5y+0o2 being able to run fast have slender lower legs with flesh and muscle concentrated high, close to tfy miny*st5, 2yx0 o.ft+d1 fkhe 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) 51 3 - )qlt1g1ypydv)fhycovicarry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If the net 5:uj7hvjvi+vtorque on :vi j+ujhvv75 a system is zero, is the net force zero?

Two inclines have the same height but make different angles witj 5y:pcqq9sy3*j 9f/a jx -sbth the horizontal. The same ba : jqyq5tjf9jx- 3ycps9/s*steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an inclins xc8xn(x/o;ka. k2nve. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?vnxk 82o;c(s / nkx.ax

A sphere and a cylinder havexgoen0vv.-/ n 8 ,idzc the same radius and the same mass. They start from rest at the top of an incline. .nxcn-zid e/vv0 g o,8Which 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 conserved. Yet most moving ou/82g;d 8 hjew+kal eqr rotating objects eventually slow down and steke /jqla hw8d+8 gu2;op. Explain.

If there were a great migration of people toward t5+gvgp*,)qpd+ s,hlziaxs l3 he Earth’s equator, how would this affect the sgil*q+g)a +p ,vlxp,d s3z5hlength of the day?

Can the diver of Fig. 8–29 do r:kfb1rh3; ii 6vz i,b:b ;fdda somersault without having any initial rotation when she 6 rhdrdb :i; ibbi ,3f;:zkvf1leaves the board?

The moment of inertia of a rotating solid disk about an axis th vjvmh o*(c, bz5-ic*trough its center ofcmhczb *to - iv,5*jv( 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 holdiv *.qva+gmd 6r be:8: zplvz4nng a 2-kg mass in each outstretche6*b qpne8 +mg4.za zv:v rlv:dd hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is hollow and thp6(sy9i- pgiits (s ;d.se9 h,ilk zb0e other is soeyt0kli;i.(gi,s 6p-id s 9z9bhss( plid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotat:xx8dj1 t5l0asmho q5 ing on a 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 linear acceleration of this point at the top of the wheel. Is the angular speed increasm :0 lj1t dasxxh8o55qing or decreasing?

Suppose you are standing on the edge of a large freely x q:ac8usj69ttp9 -kv rotating turntable. What happens if you walk toward the c:t 9t96pcqs- kj8a uvxenter?

A shortstop may leap into the air to caggsuezy+ mto,m -6f+ /tch a ball and throw it quickly. As he throws the ball, the upper part of +fomyeg zmgts/,u6 + -his body rotates. 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 conservation of angular momentby) /w:gca:xeum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate :e/ca) wgyb:x to keep the helicopter stable.

  Express the following anjvb(4q gtf-l 0q2p -zmgles 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 coincidence. Cant/wu0 4detr(ta igz5i;4si )lculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen t; t4 dz estwg5iniar40/(i u)on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directi9 l yveqm9j2.ed at the Moon, 380,000 km from Earth. The beam diverges at an anglei9y2j.le q9 vm $\theta$ (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 an-m n5z8s k2u,. yv,.yi 1ld jz7kwsky rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as 27 mnz. ,.ji1w5 8dys,knyklz -y svkuthe blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If the ball makw t 3r )9*1dcgbri.j*hxj flq8es 15.0 revolutions, whab g8.j3qx*hf* cij1drwt r)l 9t is its diameter?    m

  A bicycle with tires 68 cm in diameter trthzowb;j3(* bh + 5.sckd lh9javels 8.0 km. How many revolutions do the wheels make? jkdcbh.bh(j ;*h 3+tzlw9o5s    $rev$

  (a) A grinding wheel 0.35 m in dii00cc9y4o2fi ; /ynzdorqv5x ameter rotates at 2500 rpm. Calculate its angular velonc4520o9yri oifd c0xy;q/zvcity 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 completsu.0a/8udd:wpz6jp c e revolution in 4.0 s (Fig. 8–38). (a) What is the linea8jsuad0 /uz .wc d6:ppr 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 velocity of kju+b*t xj*q( 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 s (+2mvi1ut :lnqu- zqipeed of 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 fzn:n29ih: l 92omkuv centrifuge rotate if a particle 7.0 cm from the axis of rotation is to experience an acceleration of 100,000 : khuz992nm n o2fvi:l$g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 reqxe3g :0b5c k7qmh0hpm to 280 rpm in 4.0 s. Determine 7hg03e:qx0bk5mq ech
(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)a58 re ncobr lzf91,ks $R_1$ 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, astronautjim n gq//v9 s4f9+stus 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 minutis9f9 mq nvt sg4/+j/ue during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm in 220 s. Through :sdwp k;nh tc8 xh,36jhow many htkp3 ;s8nwxj h6cd: ,revolutions did it turn in this time?    $rev$

  An automobile engine slows down fromr;s8w bz/c, wa (3azfl 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 stresses of flying highspeed jets-7we,p0qx/3s 3wm api8r/ k9kptzn uj in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revol j8in, 9 pu- /ek/7zwst3qma0kr3 wpxputions 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 accelerates uniformly from 240dk x(rx 2imh;b4 .wsb0*k/qeg rpm to 360 rpm in 6.5 s. How far wilh0d kqe i2.wmsk(4;* bxb rg/xl a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 15v-d05lai yb6h00 revolutions before it -56lv aibdh0ycomes 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 schriqexl-g52e a s(g;m1r8o0 dhr8q*1d 4zgcar reduces its speed uniformly from 95km/h to 45km/h The tires have a diametersq(*rg8d5hoie1 2eacrmg4ghq0l sxz8 1 ;-dr of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces its speqf/l68)a,oei bc9 tckoga xj pa2 2-o5ed uniformly from 95km/h to 45km/h The tires have a diamaoa6q jxc 89 oi2pl be-t/aocfg)25k,eter 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 -g;hyky gvk 4az(2p:fputs all her weight on each pedal when climbing a hill. The pedals rotate in a circle of radiusa-k24 yhpv:ggz ky(f; 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 end of a doo *wywgmom8l9p c1 ey9;r 74 cm wide. What is the magnitude of the ;pg * c91owwe8ymym9ltorque 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 aww sw4vig 4.sw:8rqw+xle of the wheel shown in Fig. 8–39. Assume that a friction torww.w gi4q:8+srww s4v que of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a massless rod w8f/ flrx.pax, 6v 4flmhich pivots as shown in Fig. 8–40. Initially the rod is held in the horizontv a6fx /.mfp,lx 4rl8fal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening z6xng)7;:qxov sv 4sz to a torque of 38 7 qsx6nzvsz4:o xg); v$m \cdot N$ 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 inert r5ofo3 -x5zpup4o l:.ce km,wia of a 10.8-kg sphere of radius 0.648 m when the axis of rotato,cu.p4 o 5p fzmk3 r5el-x:owion is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7pz91yjdw(; ze cm in diameter. The rim and tire have a combined mpz9d e; zwj(y1ass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the c8f7,emaslp0 end of a thin, light rod is rotated in a horizontal circle of radius 1.20mps ,afc le87 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rotating at aiy,6t4ki(d/9 lmmjvi/1e)l a 4o mvv constant angular speed (Fig. 8–42). T(t/ ,dm9lmli 4kve oi6y)j4v/ vi aa1mhe 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(up uy.iy*ik wlm,bz1ew r5) 3 Fig. 8–43 a,zwyi)w (ly1u. mer3i*5uk bpbout
(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 tot: ;- ajuw q;r1mt4agnnf2se a5al 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 sqmt(c o v8vtrhq( zv:tg /h150pinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of q(t8 tzo15v( mhv0 tv:q /rhgc3600 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 un+7l .f7 lv + fpsf(dqkx*2irx;dn/bvi iform cylinder with a radius of 8.50 cm and a mass of 0.58*ii (+fks7x. /n+qf d x bvvp7;fr2dll0 kg. 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, acc9lucs.krn.a9 elerating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-driven merc7ys 6 ,dyr/nyvsa6o+h( (mawf .1r)z fc. xwjry-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 wdavy7chjm(, a y(wss6c)16/ f .+roz.nfrxw yith a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and.rq. (vs m p31b8)ihbkmn mhp- is eventually brought uniformly to rest by 8 .1hpvbps-q 3 rik(n.mm m)bha 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 bal.vs.ogue8ik g: .; mmrl 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 8dk t+h)2r irdthe action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly fr t2+ihrd)d8kr om 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, as shown k-xg: i efnm89lp fg491dlaun2/n)wxin Fig. 8–46pfg/n8xn:ed9a k1n lguw 2i4m9)-lf x .
(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 conq0qtl) /gh r5zsists of two 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 flrc +dw/+ *.x m 6ju6b;kn2jmea-akhwithin four full turns (revolutions+wnal .ekd6b m+a-u hjxj m6rc2 /k*f;) 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 ofbjb+d.g xj2r4x4 k* km 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 dr)pv6ef(l2d); lg q caevelops 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 radiquy,qut 6 e8xigk oo35-hw *6fus 9.0 cm rolls without slipping down a lane at 3.y 3qi uu6g ,x *kwooeq6-f5h8t3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to t4gahjsn x-k,t8z ckql 5)* e4nhe Sun as the sum of two tenn e,jt4lh -x 8k5 *zcsg4qka)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 has a mass of 1640 kg and a radius of 7.50 m. Hzk 8h-z:s.2 bf4sqd vuow much net work is required to accelerate it from rest qksbzu 4z2sf 8- :h.vdto 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 1.80 kg starts from rest an z9kdpntbk 4h:pp 26du /b+c2zd rolls without slipping down a 4pk/9 cuk h2 tn2:bp6bzd dpz+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 z /es;1q6gleqw : ga9ton its tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end ofw/ae ;zq6tlg9 1eqg:s the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular moment-nspf 2xij( (u/s-xmlu.en 9 itw 24ivum of a 0.210-kg ball rotating on the end of a thin str lsi4- .v mp2(inwxn9is ufxu (j-t/2eing in a circle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angul) 7t/akp; *puz4: qstjk fhc/car momentum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating at 1500jc ;pt4ps*kaz:c 7 ft/)hkuq/ 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 ratsat3(j mx1fsi*7va 0 we of 1.3rev/s If he raises his arms to a horizontij w07sta1*a( xfvs 3mal 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 i+ks4g*d*wy.m ko x 9;yzk *lren Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the *lg kr ws.m;yx+eykok9 4zd**straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin w(ose )+av6;qo zqya(il)q,c rotation rate from an initial rate of 1.0 rev every 2.0 s to a final ratel(v csazq ,q6)ioa yq)(we;o + 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 centerc nl-rfniq++4*l)r c l at a frequency of 1.5rev/s The wheel can be considererl +4*n )ifc+n-lcqlr d a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of nrf9es;n srwd1/s 0 s-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 momentp qxp,qoa8 q,,l db201wl3 da 9vytg6bum 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 dropped onto 9 pr-kp 8qz3owan identicalz9- r k3p8wqop disk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4 s))kj8 i4qmjjrh7oc 8gb/q6i3u8ls z $rev/s$ 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 rot,lje7d 5+x oxkating merry-go-round platform of radius d7j5e kl+x,xo3.0 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-g,a4z-u e bi nir ;q1cebnt;1k:o-round is rotating freely with an angular velocity of 0. itzbu,-;bin4 re qnka1ec:; 18 $rad/s$ 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 whit5b/ 6d oae)jntp bj3lh3fm)*w e dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to3*l 6j5fon)wb )tmbh a/dj3pe 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 windswqxz *yu de l;;ocoj6,muo.6 , 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 8pd4uemh,1mi$ 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 fre tcnhy+8a7vx i3*yx7 bely without frict y nt87 +xay7v3xch*ibion. 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.k cs4j;xz. rl stands at the edge of a 6.5-m diameter merry-go-round turntable that is m;.c lkz4r sx.jounted 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 n79yyyiaopmq p-bst w5wk: )x(7g)m; ground with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walkst ixawky-:p))yp 9wb7 (ys7mn;m5go q a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such th m 1- .lo+ai-timb*falat the same side always faces the Earth. Determine the ratio o1mim bil.lat-ao-+f* f 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 Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate-rk38ke9bpkwx ve )8z 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 shayqmc9qhrw-k/7i. *5nbx2fzyn* t rb0pe of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calcn5ti*rn*90yhq7qwkx r2 - ybcmz/ .bf ulate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mr4 gme,o- : +-j1xjcgxn :qrneass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diamonq : 1g ex,mj4gr+xe-nc rj:-eter 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 afq)i*) 0dyuzhngular 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 s whp v-iz4nx;+*c2 ;*pegcptwize of 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 neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentumn;i*2 -pv zw w*+e 4hcxtgc;pp.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile isrmcv y/ 8 eww*x0 d(8oya(v,mt 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 /t(mvyc ,88dv w*x(owmay0erflywheel 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 an 6ja a5f:m1/ jciha8ln $H_2O$ 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) vzya9j :gzwo-3 1h9ej is rolling 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., we ignore frictionfdpv rh 07ncdo,3)w23iww ngd ab06;f) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment 6rhb d0;c3)dawdi vw7p go2nf3wf0n ,of release, determine (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 radius R. It is standing vertically3 vix :)as nuk)av1ywflk/0q+m 6 rx7x on the floor, and we want to exert a horizontal force F at its axle so that it wi)a3lv 7 kxwnrk+ )uf0myiqvs/ 1:ax6xll climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat roadwvr 9xo2hqfs z5y9dg5bt45j. is making a turn with a radius The forces acting on the cycjz oyd2 ht bxf9554sqrg9.w 5vlist 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 in,i.1 o k +rb j,m82lozljeidx3to a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is e,.jdr m21ooj 8l3+zxlk ibi,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 rodm 7h wx-bqb:8ps, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arwpb8mh-bx :q7 ms held tightly against her body.   

  You are designing a clutch assembly which condd16 ,hlm fdpq9 ,3wtksists of two cylindrical plates, of mass w,m q1tdd f3, pdk96lh$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 t 3 rm*vik7xvp8 lka3m2u1lj n)rack of Fig. 8–58. What is the minimum value of the vertical height h that the m8*vkm3akni7 r1l32j x pl)vmuarble 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 dm4o8ddj ,xf 9+:3txneeld fd .o not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces it/oncu (cbuq /k*rf6f ;s speed uniformly from 90km/h to 60km/h The tires kcu f;qfouc6( r/*/bnhave 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