A bicycle odometer (which measures distance traveled) is attached wmv g jbe*); m,wrd(-gc1u po2near the wheel hubgv*wgepj)cuw ; (ob d2m, 1-mr and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at consta wscyzlvkov owq c c,((z4,0evjw)-* 0nt angular velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases unzcw k4,),vv0zwc 0vwe -ojq*c( syl(oiformly, 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 describedafno23np,-bw3mhukb g-5nn 3 g* wpp. by a single value of the angular velocity $\omega$ Explain.

Can a small force ev+qza84omk,l6sdx7 ukpl q y* +er exert 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 to do a sit-up with your ;/pfga3 6 ntafhands behind your head than when your arms are 6ffta 3gnp;/astretched 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 4 l.,i(zp o ghkq6-snoat the pedal cranks. In which gear is it harder to pedal, a small rear sprin(4o6 -o kzlqhg ,.psocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower legs witqk7 *nsd(ui .dh flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotatid quni(kds7* .onal dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry zo ec.; )(fg5 hj8:so3sszswoa long, narrow beam?

If the net force on a sy9fjfsmjd u o( agke-;z*8yq5m-diy00 stem is zero, is the net torque also zero? If the net torque on a system is zero, is the net force zek -0a(5u o yqsm9f;*z y8 mijjfe-d0dgro?

Two inclines have the 78qdi t15qq6nc vmm2 qsame height but make different angles with the horizontal. The same tq2q8q6mi n dq157m vcsteel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simulta3 nfz r94yrdazyx(+ xi89q0 auneously 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 t d 3x(qn0 zyrraf984z9ayiu x+he incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radi3a rxip9y/he:t/k;h9 e0 b dklus and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the g/xd tak0; ekyl:rbhi93h9 / epreater 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 mostji3 sf ./nkz5s moving or rotating objects eventually slow down and stop. Explain3nz.5 f/s ijks.

If there were a great migrat+o/ 8xs5uelk bion of people toward the Earth’s equator, how would this affex/k 5 lbue+8osct the length of the day?

Can the diver of Fig. 8–29akoeis9q) +o mq9i2:em;e(0oba /ehh do a somersault without having any initial rotation when she leaves the bq0iomh: 9e / miooekae ae9;+b sq2h)(oard?

The moment of inertia of a rotating solid disk about an axis through its cen 8etzk ud,5q8tter of mass is ,5 t8dq8zuetk$\frac{1}{2}WR^2$ (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 onprxu-gg75ml-; h* wpl a rotating stool holding a 2-kg mass in each outstretched h5*wu - p- lmhr7gxg;pland. 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 x m udb(poip2/pwxlg+8)y 2uw6*lzk,mass. However, one is hollow and the otheu i(ldbyp+8x /wo6)m2p2klw x pzu,g* r is solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle poiy 3,mz5khcu c3+ efvb5nts west. In what direction is the linear velocity ofvu5kcm5ze3 3b+,hy cf 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 on the edge of a large freely rotating tubr sz0au pn9:(kc8:ne k45xnqrntable. What happens if you walk toward the centeru(s:b:kc ne ra489p 0q5znxn k?

A shortstop may leap into the air to caifz8 ie77jkm6tch a ball and throw it quickly. As he throws the ball, the upper part kiij67m8f7e z of 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 momentum, discuss wh,g j rsnu/)+ioy a helicopter must have more than one rotor (o ji/go+s)n r,ur propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the followin93j6gh, 3mkaacd pnps4cw8h+g angles 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 oa2 fiee gp f/h3-)g sc9+-huavf an amazing coincidence. Calculate, using the information inside the Front Cover, thhe/u3sg)g9i- cpa-vfh ae+2 fe 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 Moown nxk62 7raj4n, 380,000 km from Earth. The beam diverges at an an6j2knw 4nrx 7agle $\theta$ (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 t- l1p1c;z zwlu6- zx)h5nlyb m+ndi* lhe motor is turned off during operation, the blades slow to rest in 3.)hulnc-iz5; -zn+wm6 x *zpb l1l1dy l0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball ; z(svx v :ut*j5jgd9fon a level floor 3.5 m to another child. If the ball makes 15.0 revolutionzj s9u dxt:fv( 5*jg;vs, what is its diameter?    m

  A bicycle with tires 68 cmr)(cy,w f anc iwx-ak s0t)*r l5l65r,hhij9o in diameter travels 8.0 km. How many revolutions do the 0,aa-5tl9l* )xnh o)s5f,jir ycr c(k6 wwhirwheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calcu+i3n/guf gawe ml*+;d late its angular velocity duemni l3fga +g ;+w*/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 c* ajit gb5.bm9a0v b : ppgdadqc*/g;:i7tn7s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m from the ce7 t0;viic7a bgjn:* g.:a ppq5mc/b9t dbagd*nter?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular vela:rlgnb3pe-g6 67td 8e.cppa: je jnl7 ll4-docity of the Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a -a1/( h4ifkgg;f+ :mlho: 4m,fwmx z k5 byxclpoint
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rre1l 9zyp7zc fpr9i ,pl oy/2q) 05akootate if a particle 7.0 cm from the axis of rotation is to experience 20ezof,p c )y9l payk15 rol rpz9i7q/an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about itqza +n r..9 ippofb czpa(86n/s center from 130 rpm to 280 rpm in 4.0 sp/ncnbzrpaf 6(i8az9q . o.+p. 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 1vtvuv, 64hpc$R_1$ 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, asty++m -3gx v4b: rwvz o i(o.sagm-5eamronauts 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 revolutioyr gs(3be. a a-m45woommg:v++ z-x vin every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 j* 1)md -/fqfhvh x dk*+m(.d*am lcwkrpm in 220 s. Through how many revolutionsdmk-da.c) wm *qmhf /+l*1k v (*dfjhx did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1ytkd 6nxtouyk2 0(nj( u0rdr (0dd-gif+/5 hu 200 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 .yt b4a6( zhho7qkng5oei3645pla x-8uyko hfor the stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reachi eyp ix 746oahlkuyk b g3nto 48(h65-5zoaq.hng 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 mswg d6zg;7lrca12; l9l:xcwfrom 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have travel7cglc:axw91g s2l;l; z d6 mwred in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 1500 neutr8c/,n / bous2 :irevolutionsc tsir,o: /u bn/eu28n before it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions a5lv i; .hrh(3a)fwi jgs the car reduces its speed uniformly from 95km/h to 45km/h.i 5alhv3wf(gi; jr)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 revol484 -,op uobi 6awjvupc:j7bp utions as the car reduces its speed uniformly from 9 6apu4w ovbpj:4 o,i ujb-8cp75km/h to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on eac+mku hktkao6v(4( d h9h pedal when climbing a hill. The pedals rotateh k(kuo+a k4 tdh9v(m6 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 end of8aki hvmox8ndqdr 3*g 1 -j;u;gn6j*m a door 74 cm wide. What is the magnitude of the torque if the forcd8kg-;ar*;jui1jdg xm 6om3n q8 *hvne 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 pe .3o;0ilwg5ss kzu 2the wheel shown in Fig. 8–39. Assume that a friction tor23 owsigl;puk5e.s0 zque 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 8acucf/s 4 j f1;j2ogmof 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 magnituag js; f24mc/cj1uof 8de and direction of the net torque on this system.

  The bolts on the cylinder head of an engi7 lmofgrxtc-ef0 1(t ,ne require tightening to a torque of 38 -x (0lf,gmcteo 1rft7 $m \cdot N$ 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 6i3iv jipqbjv:. 8.ah of a 10.8-kg sphere of radius 0.648 m when the axis of rotation is through its cent6javi :pqih38 jb..vier.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle whyz6g6m.2zq q qeel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be igyqg6 z6qq2. zmnored (why?).    $kg \cdot m^2$

  A small 650-gram ball onf kw **kannj822g6dhn the end of a thin, light rod is rotated in a horizontal circle of rad**nkn2fk6djwg 2hna8 ius 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 h; ).wkcyr-09i1nu kgnmwq ,jwheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and the clayjukmng;)ck inh,0 . y-qw1r9w 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 oj 9 jby3g9si8yc e6h8if inertia of the array of point objects shown in Fig. 8–43j86 9 yc8gbeihjysi39 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 rp+-orzah(ej5xw. 5 q atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning0v t+rqq2* p le s oq+0.fxl3k2+vrbyg 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 t qqesb2k p2yl+ro+vq+t0r*3x 0 g.flvo reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm and as(ez4 jek9zk 1 mass of 0.580 kg. Calcz (szeje419kkulate
(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 3 qlpj8;m/u0r +zmtqzit from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-driven merry-go-ro4kkqp l;vq.- tund 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) sit opposite each other on the edge. Calculate the torque required to produce the aq;qt p v4l-.kkcceleration, 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 is eventually broughkw 1nw ltmj15e5ww4+ft uniformly to rest by a w 1451wkwe f+wln5jmtfrictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a 3.6-kg ball 9yh/ 3sbu0 oqdat 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 6k;okob8g* bt8i-fim is thrown solely by the action of the forearm, which rotates about the elbow joint under the a 6gb 88;fito-*omk bikction of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a xw cp:y xw;jy,t//: tclong thin rod, as shown in Fig. 8–46w,p;/ct/xjcy::x yt w.
(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 mass0xf)jq sf p lv:6kl66hei47dn es, $m_1$ 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 4 muzq: .remdokmi,2a3 z9/anfour full turns (revolutm/rk ,undq.ima e2a: 94o3zmz ions) 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 mom1w)vhhiw4m ou4pm/ i8 ent of inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torqu/qc/m s,kt /6fm8/tbed:yuube 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 rocc r4.ni7i m8 d(yv/eflls without slipping down a lane atd4nc/.mr 7(v8fyiec i 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Eartrhb6i0 mci)w5h with respect to the Sun as the sum of two teb)h6rii wmc50 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 a(kkgv/: hhjp7,w4 ;b)nvsg mpnd a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s?kb 4v(g 7 )mhh;pvpk :/nsj,gw Assume it is a solid cylinder.    J

  A sphere of radius 20.0 jsn2q k-kh5j raff i-*,ugtk/od3f6.cm and mass 1.80 kg starts from rest and rolls without slif -5t au*q6nk-gih2d. r 3skofj /fjk,pping 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 vertically84 4btiauexqfy o 84:i on its tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits tq 8tu8fb :i 4ae4xyio4he ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating os //jcnx3 m8tan the end of a thin string in a j c8atsmn/ x/3circle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular m)79tip3cg6,+ls h zsf ;lt jzxomentum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when r6jxl fzp 39l,hgz ;ttci 7)+ssotating 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 plp wbw6nsu23m+- ttf2aw* p/t 81rl usnh(, hkjatform that is rotating at a rate of 1.3rev/s If he raijatm81l /-rp +ut* nh26sktwhf(w3w2,sn upbses his arms to a horizontal position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one showaql0uk+4q f wb6f9y:t y8dy:i n in Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotationb0 lq8t:9:+ 4i6wdk fyfyuaq ys in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial rate oxgvs i+e995eaf 1.0 rev 9xve9agi s +e5every 2.0 s to a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axis 0ttf pg(tocj qdn) 8i))d7) 56plkwqy through its 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 q65(y) lwoptc fn q7)0kjittd)d)gp8 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 momentui 8h xn*.am d26u8ezm4czl sr.m of 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 mq2uigc 0o c32komentum 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 cylindricaw32 ;vyym16wi4j hiufl disk of moment of inertia I is dropped onto an identical disk rotating at angu;yimy1f2 w3hw4u6v ji lar speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.45 bg7/v3onlslc 8)h mx $rev/s$ 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 platfh foc *dkr53 5amvg52xorm of radius d5grmvf3o25 a*kc hx53.0 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 an t *lzjt; 4po2 cfln01zjwc )2oangular velocity of 0.8olp;2 tf 0jl4 c*n1jzz )2otcw $rad/s$ 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 eventuallys)s5 *ue4q3lmbp/ft(dqci1-z 8t hml collapses into a white 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 angulard3 mlzbq*p45s /)se18q(ttifh m clu - 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 ws5wxg4 m/4f/dy8w +vvurbv,tinds 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 6dp6etsd p) 8v$ 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 freely ,lo2*yve p4rtwithout friction. The moment of inertia of the persel2 yv*,ptro4on 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 standsa2kevic7ey 8+* (vuh i at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearingsavi (2k 8uv*7+chei ye 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 05)jn t2tutdp 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 j2p un) 05dtttonto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always facesf(69xyzx/ o * i6uwjac the Earth. Determine the ratio of the Moon’s spin angular mof/xjz o6*6 c(yxu9iawmentum (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 atmln4,by/v 3x u a rate 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 0.20 m gj qjn*w+;p k:dak+su: bo++d acquires; *jd oj+pug+sb kq::awd+nk + a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.u278pwk g4zu(yl. rov 050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it rku gzwpl4(ur 7oy 28v.eaches 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 wr/rpcvjt t,59 heel ($\omega_R$) 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 mass 8.0 times as great, were (ceqj:chro*u l0x(/h rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse lr/o j :(hhuce*0cxq( to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use ef51t2ppy+o j. 5x;tah*a fgz yetr1w)nergy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diametteyx5 +t1a ar5y )p;.hzw2gf 1otf* pjer 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 illustrat w+dzyumak86 ed9wc(6x nc(i) 6 o7gszes 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 on2n dhmje5f cb0p*.l x1 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 lengt s. bhl6u y(5hrsbhvu7k/x m9kv08)ayh L can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. Th.ymb ) krlaxs08/vv7h b9su56uhy(khe rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume 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 verticallyajvi:4fq 1u,xbfb 3 p0 71tktt on the floor, and we want to exert a horizontal force F at its axi01f,ub7k1 tt x ta4:jq 3bvfple 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 speed v=4.2m/s on a flat road is making a turn wit.( ohc (4lsxuyh a radius The forces acting on the cyclist and cycle are the normal fory( u.x4cosl(h ce $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ 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 1.5 m and begins whij* *;tfl4/wf( ax uenjrling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. u f4t*nj ;jx/w(fl*eaWhat 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 cn 1b b s-:oqw*lcd7gl.u42ecwylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly ob2 .bllgse4dcw*uwn7 q- c1:against her body.   

  You are designing a clutch assembly which consists of two cylindrical plates, ofpzpzz g)xkp ,,uf,y*p(p1i( p max 1ik*z, pz,fzgppp )p p,u((yss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 trachl 4: 85k+kk* ; q+sbumynqpszk of Fig. 8–58. What is the minimum value of the n qmhp8k k l:+bk+sy*qs 4z5u;vertical 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, bwhtl27eqw v zs 4te7dd.l:a: )ut do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as1;vy( entb0a+ d0 zayw the car reduces its speed uniformly from 90km/h to 60km/h Th( vdzy0;0wn b+e1a yate 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