A bicycle odometer (which measures distance traveled) is attached near the whe3 v3h8 nrvvrg5el hub and is designed for 27-inch wheel rnr38 hv3g5vvs. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at ciyj4v86l jw k4fz fs*8onstant angular velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the poisjk fv8w y86zilf4j4* nt have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be describedn31ds +y4m: xc tvw9ck by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Expla v,5)ght8obihvi 6i(fin.

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 dopc- 5bvuvt+s). ye+kx a sit-up with your hands behind your head than when your arms are stretched out in front of you? A diagrapkb5uc +y xv).e+-ts vm may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel an/rck 5 yl suc.lq76wkqw3ns46d three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprows kyql. ln7 r3q/5ccws66uk 4cket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being a 96 nfwuw(4zhx gkturj8zf)i(gp80 i(ble to run fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the bas ruf n68z4ui)8x9g kp 0zjt(ih(wg( fwis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a */ddwtujrjeb- ;sz*i dq ,u41long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If the net t dqky*,1pis +torque on a system i,dkqt 1i +yps*s zero, is the net force zero?

Two inclines have the same heigcrf+ xo;7t fl,ht but make different angles with the horizontal. The same steel ball is rolled +,crox;ltff7 down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneousls7k6bqjmm5iid v0 .7+m eek7by start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the b+iik7 mmsb5.kmvede67 bq0 j7ottom of the 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 radius and the same 0.pwu)f(7cnhr1 :zan2em ni xmass. They start from r r1wxheanp. fm2zn:u7 (0in c)est 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 moment1nw9t (9btm hkum are conserved. Yet most moving or rotating objects eventually slow down and sto ( ntt9m19bwkhp. Explain.

If there were a great ras 66jk*1ahe4k qlw.migration of people toward the Earth’s equator, how would this ajs.l64*a rqw ah61kekffect the length of the day?

Can the diver of Fig. 8–29 do a somersault withoou+suk9/y )ca .b0t miut having any initial rotation when she leaki/ts 90 uyao.)mcb+u ves the board?

The moment of inertia of a rotating solid disk about an axis through - 0b70 xt64g izcifag. qm+ttgits center of mass m+6-4ig. fat t0gqbitx 7c0 zgis $\frac{1}{2}WR^2$ (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 eachfwngl3xt5 a +1 outstretched hand. If you suddenly drop the masses, wgx5f3at l+n1 will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is hx5n1+pld;yy l ollow and the other is solidnx d;15p yy+ll. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle point*y;i+kd2qwgzu0 i m f)r g.w-c50pf eis 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 acceled0qwe2 +g* fmp;ki z )f gy.0rcwui5i-ration 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 larfr3 gss0du/jz ;ue )v+ge freely rotating turntable. What happens if you waldgu0 u; +v sz3sf)jre/k toward the center?

A shortstop may leap into the aird(xr t:ywa g.alan 2txb:hnf;s.j 2+, to catch a ball and throw it quickly. As he throws the ball, the upper part of his (;rs l.:afatd+gx w yhn anx ,.jb:t22body 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 conservat+fx-9nk4ijhyo9ve rn* t:nj* ion of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can oof9jnein : *h *4rtvj9x+- nykperate to keep the helicopter stable.

  Express the following angles in radians: ge 42 g8ykba+zw wb.9k(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 becausvuixxbzzc d67+ s(os7sq 7:mq7 *wt,ie of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in r 7,sowq67(x7:sz+xuv dcqtsm7ii zb *adians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam37s,*iqr +, mjg;rgjgx e 1gk5ck pgd- diverges at an angls,;ggx gk+mc5gir-,pgdr 31 *k q7 ejje $\theta$ (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 the motoyi) 3b9 ue/4+af+wzezz6 qog vr is turned off during operation, the blades slow tge +bz6 )/wyz z+ivoau9 4qfe3o 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 another child. I f qlva21mvfrh2j06m7 f the ball makes 15mhl 2f2q 1 mvr07jfva6.0 revolutions, what is its diameter?    m

  A bicycle with tires 6).z i.t hl:qpq8 cm in diameter travels 8.0 km. How many revolutions do the wheels miz )tlpqh .q.:ake?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500f7ink2f6 )iqi rpm. Calculate its angular velocni7k)f 2 6fqiiity 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. 8–38)mho55 :om+zk h. (a) What is the linear speed ofh o+5kzo5m :mh 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 fi.oveb(vlen x/,.gk -.p j-xqa-/ pvvelocity 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 poi puu(j+4e dl-lnt
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 cm from the axis ae8 zf8n55gj*ywur 2cof rot5f288yj5erg n*u a czwation is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its cente(dos9vjywo z ,7v ju(x f)e:,sr from 130 rpm to 280 rpm in uzyj ,v7 :,oewdvo(jsf(x s9)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 radiuqry *5tx(zf o6kvs k/3s $R_1$ 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 abop69 :o ien2kmrard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated frorio n6mp: 29ekm no rotation to 1.0 revolution 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 rpm in 22lb8 9 sme(dap80 s. Through how mlpbesd(8m 8 9aany revolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 125-xisutl(l/im8wn2t ;9qoby 00 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 highspeeds*vlzy46 e 3u+ lt a7 2mrjgpq/b+amm* jets in a whirling “human centrifu4+76ztmely2j/bmars*g u al 3pmq+ v* ge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 rpm to 360 rpm in 6.5 sp z imn+n9b,7o. How far will a point on the edge of m,7bozpnni 9+the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 1500 rv1 ilvvoe th7i 7,i:w/i3yzd7evolutions before it comes to a stop.1zoiyd7v:th v i7/lw,v7 iei3
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed unin11ol,ct a vv0g )ats3formly from 95km/h to 45k )1 ,al01gvvsta tc3onm/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 1 e,*:ua t9k ,*rg wca,cjf4d6xlegtl revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter ofkj wgltt, l c4fa a9,u:6e,c g1**erxd 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on each ped)0o/dzxvek4a3 m ppc -al when climbing a hill. Thx)3dm/p-e0 4ocapk vze pedals rotate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door ;frl y2ltwtpk eocpar)nd ,)24)v 1,k 74 cm wide. What is the magnitude of the torq,,dr 22y rk4t1ppkl)ltcev f) ;a)own ue 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 aboq j+hnpq n: c6bbw: q02ibe2z*ut the axle of the wheel shown in Fig. 8–39. Assume tha 2*eqzb2:n0 hb+pwcnb jq6:iqt a 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 attached to the ends of a massless rofq:+;i -ob8v/b r: w7bdujjk yd which pivots as bdv:: +7riq 8/kjjwfuyb-;b oshown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening ta9)t silg.fg3g,zm;k eh 5z v6)mhm7uo a torque of 38 za;k3 m5mg)f. mi7he6t)ghv,sg zl9 u$m \cdot N$ 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 the mue9ujx7, p3y axis of rotatix 79,ymu3ep juon is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. e((g0yrusx1z nb 7dl:The rim and tire have a combined mass of 1.25 kg. The mbur(07 (xzdnlsy :1geass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in ; xu+fu*ou;gqa horizontal circle of radius 1.2 m; +u q*u;xgufo. 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 oho2nr jnn 0g67n a potter’s wheel rotating at constant angular speedj7nro 20n g6nh (Fig. 8–42). 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;mm9/pl6uab c ygwd 2(ej2t :q objects shown in Fig. 8–43pd 6m2lycb( /m g2tje u:a9w;q 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 c4a) 3o+9grju ekh)qor2cylu wi,- lp1 onsists of two oxygen 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 satelli, u(,oidkp vd8l8w ve;te spinning at the correct rate, engineer(dk p,l,vv 8u 8dw;eios 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 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm arz9e(h/ ncw.e t,of; ond a mass of 0.580 k.hnf9;ze/cet(w oo, rg. Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerating it from restmjzc3 o 6o42tfe m;sxy2rx(;oqi+;nz 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 aror 868p ecztmc9s0 g:1 deb5a small hand-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) sit opposite s89r 6mzrgp1 08 ecae5t:b cdoeach 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 and8ncn+ ax r*p5jw+ rf,a is eventually brought uniformly to rest by a frictional torque of+n cwa5 jf +rrpnx*,8a 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-kghq )wo+bs)i2 b(fykk )zdr /(q 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 actio jm(08s6ztp zf)lyge3n of the forearm, which el 8 fj)y3p6s0 z(mgtzrotates about the elbow joint under the action 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 aq eru0, rb(0qs long thin rod, as shown in Fig. 8–46. 0uqe(0 rbqrs,
(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 masse c1af9yij46u hu. jz0ks, $m_1$ 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 acce25;fxi apec.w6g q 9,e)mom yelerates the hammer from rest within four full turns (revolutions) and releases it at a spe,efw6eae o 2pm.i qgmxy)c;5 9ed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of inertia a 1;n.aszr;s tof $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine de nrfzm0ojo8omrw4-i n8( um g.-j;:ymvelops 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 radiusq)3 re dq)5jfx83j 8 b;urlkzq 9.0 cm rolls without slipping down a lane at 3.358jr)fzb) 8qquxrelkj;qd 3 3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sunaq)r) 9.16 fhfz jncday9 :mlc as the sum of t:acd1zf).f )9 6mjanlqy9crhwo terms,
(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 164/)ip svj3*qqvsb(4i+ vbh5c z/hmtue,:y+vh 0 kg and a radius of 7.50 m. How much net work is revb+pv+q /qh /scij:vhh 5set4z* v,um( )bi3yquired to accelerate it 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 1.80 kg starts from rest and rolls wiy2:i du/3z8hnqte 3(jd lofeto u2)c ;thout slip8h dizjl2n/ttu c o;f :o)q3u( yede23ping 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 ve afgm;l;wc (fs6 u0vq*x) vs+drtically 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 the ground? [*fqal0v;( vu ;wds6fxcg m s+)Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotatingozzuyro616jj ;8 efm- on the end of a thin string in a circle of radius 1.10 m at an angular speed j-1rmeo8z ozy u6j6f ;of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindri:j9xwagrwp vjp9tinrr 6j27 d, 0 c-5ecal grinding wheel of radius 18 cm when rowptrj 6vj nid9a9pgc0rexr 7- 2,:jw5tating 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 x,1* e /pqp pcmz(nno*njc09tat his side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal n*/epx 0(9 onmpccz1,jt q*npposition, 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 gwow s2l+s1npl 2f.s4one shown in Fig. 8–29) can reduce her moment of inertia by a factorol+ p4sss2lw2 1wn.f g 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, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can zd-96nkmaa g efs+vz( . je8(yco:5qvincrease her spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a final rnc v ze:s.jg+-a ( 9zf5yd(ka8v6qemoate 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 arouwi/haijnr;:h/ -0y s (ey kse+nd a vertical axis through its center at a frequency o0nw(yy/ h +s;erk-heasi i:j/ f 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 the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular mo)z p7i )ln7kktmentum 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 o/; (qy+*zmeo v 3wil ,pciao:momentum 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 droppedqnmlq72- gnuu +6z kq w sdqs2*s(7pb: onto an identical disk rotating at angular spk u2u7+-qp bl (n6:nw*gsdq2 qm7zssqeed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns s :z2yvny -i(*h9uqzf at 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 /u)qyce1 gsw -3jsmd0 a rotating merry-go-round platform of radius 3.0 m and moment of cs )0swu-d1 y3me/jqginertia 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 freelxn+o6d3w/i6 djwk 8bt y with an angular velocity of 0. ok6+t6w d8wx3bi/dnj 8 $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a white dwarf, losing about half iqn;rq e( hbwx 1rl4-qfvq8x(6ts mass in the process, av6w qhe-( 1rn(b8lf q4 rxqqx;nd 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 to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in excess of 120b seu0gob+k. smr.:*k x;ek w* $km/h$ 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 9beve,mdc w7 hbq,92m) 1upuj $ 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, ;-zzc )x5hsu)eygf0 mthat can rotate freely without friction. The moment of inertia of the person-5 m; z ehyz)0ug)xcfs plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge oy 5c+1x7vq tvfs25f cvf a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of incv+5 5v cfvs7x1yt f2qertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the end of the rvsc+1 bdaad (:ope 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 slipping. What length of rope unwinds from the spool? How far does the spool’s center of abda(s:1 +vd cmass move?

  The Moon orbits the Earth such that the same side always faces thxsldlmyw*ji ;: p9 j-: v7zae+e Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the lattex9w zi;p s+7-*: ajeld:jylvmr case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist acceleratesi 5qg4mqx45y a45e9ejvvc2 th from rest at 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 cylinderh, v.vg w:q8x68td jqg of radius 0.20 m acquires a rotational rate of from rest ove. wggdq:t 8qv68j x,hvr 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 cylindric6vm5*dw 6 eihc.p-5qtlyw2dkal disks, each of mass 0.050 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 ene6 l5 p-.tiwdvec 6w2*mh5qkd yrgy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the rear whezhyq1 vsb qe;7n5tyj h1-/x.mel ($\omega_R$) 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 c9k4dxv0j1zp/ but 8(nwj6 brd 1c2ixof 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 an/9kdvt(x8cn02 bxr wzbu1j4dp cj 6i1gular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use energy sto6.tzq 4l/bo ijpyu9q 9red in a hea iqqp9/j .4 6oytl9bzuvy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrates a e/bsn24r( o adb2x; uuah9.wyn $H_2O$ 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 speoqx4pubc,21cz)- g e ved 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 (ob me/q q-z05bi.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 releamze5b/ q0-b oqse, 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 vertic:) dzd of.n3a0j0nwe 9ga 2ksdally on the floor, and we want to exert a e 90w)o32add j:zfsn .dnakg0horizontal 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 speed v=4.2m/s on a flat road is making a turn wi o. 3atqmd-dcpmc .a0 nu5r5o1th a r.5mutd. naqp1d0 co m5c-3o raadius The forces acting on the cyclist 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 lengthz a 5w1:.sd*a htatfgjxy (s. n-)vaa) 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torqat:anwa.)zj *t5vx) 1(ss-agfdy h.aue 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 heraf y;lt64oij1 arms as thin rods, making reasonable estimates for t ya46;l1iotjf he dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical plaxmr95i d78q bq6bg .rhp9qs 3qtes, of mas 9 q8qq3rgpxd579hri bb.mq6 ss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 f :/cd8y k54kk1cjfk2jrj yo5the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to rck1jykj f8kk r cdy:o5 /jf245each 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 ass 3 l26fdhkwnk6ume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions 5 ia)e m)rt03z6 u)ygh1npwadas the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of each tireyd3h)zu )arm nie)g taw0 16p5? $\approx$    $rad/s^2$(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