A bicycle odometer (which meabxoy/z* m3(jfsures distance traveled) is attached near the wheel hub a*fo3j x z(/ybmnd is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point x2-qylqvj-ip7tscdp* 2m/ +k on the rim have radial and/or tangential acceleqi+qsj- xd2mtk *pv7/2cp- ly ration? If the disk’s angular velocity increases 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 value3cjm 173 d:6aqd9ue he :zdazp of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater p5s+1*,jtucpzreh(z 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 nl /vp: o6g p7o ;at9wcxqv7/cto do a sit-up with your hands behind your head than when your arms are stretched ou/:9acpo v76 oqg v7plc/nt;x wt in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at t(lwa 2:4 cw8ahxwb uq u317ehrhe pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a smw7ar 2a3c xqhw4u(b8wul1: heall front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower legs with fleshu -1vr3m 7jqd3.didmki* 6o em and muscle concentrated high, close to the body (Fig. 8–34). On the bamq71ji-r d*ouv 3md.6kei3d msis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope wal (dxig6c/ho,v))he sp x0sk/ekers (Fig. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero?povbe3c+ d y-1 If the net torque o1+- p ybcode3vn a system is zero, is the net force zero?

Two inclines have the same height but make differentc*ut3-viw,a 3 zvnnobj gi5.+ angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed -c3ni+jubn3* ,g tiza5wv.ov of the ball at the bottom be greater? Explain.

Two solid spheres simulta+l*2ubm(t io(o/kn:dg + wggg neously start rolling (from rest) down an incline. One sphere has g no o:twig(u/*dmkbg+l+g( 2 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?

A sphere and a cylinder have the same radius and the same +y,;*mkkria,)qyw ztmass. They start from rest at the toiqty mawr,y)k ,+*kz;p of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved, 27d nvr ykfms5x,*rg+jb.eb. Yet most moving or rotating objects eventuallysrx dj e7.v, +n,ybk5*grf2mb slow down and stop. Explain.

If there were a great migration of people toward the Ea 0px zcdgevgq+ti bt7pr 81,j57mu((zrth’s equator, how would this affect the length of tc0bd7txv+ti1 ,((puq75 8z pmzgrj eghe day?

Can the diver of Fig. 8–29 do a som4y9(tod c hs2mbcb*8 oersault without having any initial rotation wh8d(c4 o bhtomys29bc *en she leaves the board?

The moment of inertia of a rotating solid disk about an axis through itz/,49f phhyk xs center of mass is xk9y/zp4hf,h $\frac{1}{2}WR^2$ (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 r g1a3g4 fgok2qotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, wa1f3g g2k og4qill your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, ozy ;oh/y(4sxla:w (x nne is hollow and the other is solid. Describe an experimensx4yx:( (awz l/ oy;hnt to determine which is which.

The angular velocity of d2r6 :3kju84h kkgtpha wheel rotating 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. Is432 r8kthkd h jp:6gku the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating turntable. W*ca ,7py t.mythat happens if you walk toward the acyt7yt .mp*,center?

A shortstop may leap into the air to catch*.9fjqprmm9 ysfk.2 h a ball and throw it quickly. As he throws the ball, the upper part of hi2h9jfp ks. *qfy.9rmms 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 why a helicwmsj5hecqm: dl/aw90qw -; 0oopter must have more than one rotor (or propeller). Disqw:;wwslq 90jh/0ae md-mo 5ccuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians: (a) 30a fpgf:tzw+ .s,: oe,w $^{\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 Ea m;uw316bdacj rth because of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Ebu3a 6jmdw 1;carth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Ear4i; .i3 tmlg+ :saduipth. The beam diverges at an 4 ig.+;ti spmuid:al3angle $\theta$ (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 i hxd, vc)p58 -wc/bamu/sr g-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 the blades slow d//x wavg,dui8cscb-) rmph -5own?    $rad/s^2$

  A child rolls a ball ongz g5veym 7 hl1r/(to* a level floor 3.5 m to another child. If the ball makes 15.0 revolutions, what is its g/ho ye(g1t*mvrzl75 diameter?    m

  A bicycle with tires q(h zruqzz n)5u 9/x/f-e,mig68 cm in diameter travels 8.0 km. How many revolutions do the wh)u/5-exq9, z fiqnhgmz/ z(rueels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 k u+5cj:hlsoo5:kbc2 rpm. Calculate its angular velokoo:55j k:lsc c+b 2uhcity 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.vr 32n dc-*zhq 8–38). (a) What is the linear speed-rn3hvcq 2z *d 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 the Earth (a) in its orbit arou(n 5:w boe2edynd the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear spet4w,s sh2cthul7: (: 7tv *y2mnrtrpded 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 centrifuge rotate if a particle 7.0 cm from ta4; l .xh +r.j7x wvki)mrahe8he axis of rotation is to experience an acceleration ofv.7a4+ahlrkxx w)r 8ji meh.; 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about i 2cs/:4h wcdf0nyci2uts center from 130 rpm to 280 rpm in 4. whcc4cs:dniu/f 20y20 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 radiufhw+-a1 p1vkp. uto2 gs $R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$

  In traveling to the Moon, astronauts aboard the Apollo spacecraft put thems2rbfs kw4 s4i03rty 4lelves 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 evs3 kt4 lirbr442wfy0sery 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.b*pnjw1 w4 r492qnrdt t ipu- rest to 15,000 rpm in 220 s. Through how many revolutions did it t r2inn*t4b1r49uqw w-p. jtp durn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5ltgq8 ) ;rjnm0iomd 4vn tzqez)(9p;8 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 testedy,id,v/ x7ccm. cb,jc for the stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching ibvc ,i,c/,ym7.djxccts 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 rz(b l4q;u 5kov419 rkb7z ctxnpm to 360 rpm in 6.5 s. How far 4zk7ql 9kn z(b4u1 c5o;vtbrx will 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 urwiu(:bk ic3t) /gw1),dxmd 1500 revolutions before i)bgu:du, t)dw1 /wixicr3k m(t 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 as the car reduces its spede*q .d ,5cwjom j1cx7ed uniformly from 95km/h to 45km/h The tires have a diameter o7,mc j qd.*x j1edcw5of 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 6fitraw--p+oc nf.7st.+ fzm :s/uilthe car reduces its speed uniformly from 95km/h to 45km/+s6wzfto/i. +tua -l-m nrffips.:c7 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 each pedal when climbing 1rb*()seotn+ ;7fmo zz es*lza hill. The ped es;sr(z*zn7 zo +1lmtfobe*)als 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 ufn(q.wmw +1u *rkh9u;qs o8aend of a door 74 cm wide. What is the mag su+ k;fqm 1un q*a8(uo.rhww9nitude of the torque if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle ofux1*k ox i;te. the wheel shown in Fig. 8–39. Assume that a friction torqueei ;xuk*.1t xo 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 aw ;w9o /oug;zg massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate g o9uo;;wzw/ gthe magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening to a torque o186 nt c(bs8* pbcz4cwt.t6-dnhgeqof 38bbtzg6t16cow8-48t(d.cn p hcs* qne $m \cdot N$ 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 spyncm7i -,d:dzg m y- bqh)5pq5here of radius 0.648 m when the axis-gd ,h-cnbd5 q mz)py:m i57yq of rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inerr(*+ll hjzqh7;lwup ur1 8)h stia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combiuz )ljhh+l p8rr;1s(q7w*hul ned mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball x(69i5vpnfvp7 u0ag:hwr 2lr on the end of a thin, light rod is rotated in a horizontal circle of radiu6 0:5rganxl whv(vr2f p7ui9 ps 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 9gfv+ lr g ;g43uvk7cbpv2. jwwheel rotating at constant angular speed (Fig. 8–42).9 2lk vgfwg+grb3vp7v .jc; 4u The friction force between her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of point objects shown xr tski .n c2io2,3qii1 8e.zqy.wpc*in Fig. 8–43 aboeyzqi.xnt328ipi*2 .1csic, . q kworut
(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 roo3. ckl:t:1y+krx jal 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 spinning at0 g/ /x7 z gzvi00tbi39ouhnyk 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 ri/u9kb zvnoi /xhggzy 0t3070ocket 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 and a mass o,l cv bil8:bu,d8,; r-fe mwrxf 0.580 kg.b, 8bwld-,mi:;,u rlr c ex8fv 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 f v0r myc5 .wptm:ab vbks;).3zrom 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-drs 3n/)z tyti*-hr(q friven 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 dis t sqrz/nryh-i(t3)*f k of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotatingipu* )fd 6k;km9jkx 7fg7lbu( at 10,300 rpm is shut off and is eventually brought uniformly to rest by a frictional torgu 7;m *fk7b(kk)jpf6i9ludxque 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 a xgwsop823e1s v n (noyx14;beccelerates a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action of thej zal3-96o w7tg(-zmj:jarma forearm, which rotates abourj gjl -aam936z(ot :-m7wzjat 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 c8fie2t0 dfu7lan be considered a long thin rod, as shown in Fig. 8–4 ef287tdl0ifu 6.
(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 masses, 6;b4y: soilb v$m_1$ 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 accelerathonp yia.2 -0 due8s0kco7m8wes the hammer from rest within four full turns (revoluc87u.ay -2n80 e oikhod 0swpmtions) and releases it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of iner jndrezz889 )z)db98;3h7svnrzmoon b snu/)tia 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 *hhpuc/a;+ t-7:2z t(d scnirnf-rmr a torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm roljsvgy 8tot76vow1t0 dcm, (8mls without slipping down a lane,s8m tot 80m(7t1ydo6 wv cjgv at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun0vu-cqq1un7 yv (x0qq as the sum of two -q7 x0q quvyv(n10cuqterms,
(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 h.ff 6nkmhp89 7.50 m. How much net work is required to accelerate it from rest to a rota mfkn.p8hf9h6 tion 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 without sr 0o;q, h*qgqtlipping down a 30;0ho,gt rqqq*.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 balbfe m zm6c* 2pa7/y3wlanced vertically 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 h6*ebcp ywml/f2z 73maits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on 5;drmu*a7m(fo )d rdb the end of a thin string in a circle of radius 1.10 m at fd ud(m*;r)mr7 obd5aan angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grindzjdf7u 3dm)i 6ing wheel of radi7)idfjm d63z uus 18 cm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a plaj*4w is;2 kzyrxw3ya/-qs e0ff 4kp )ftform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decreases t ksfj e3wsf 4x2y-z)wy ik/p;4*afq r0o 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fi sex 0 69*om*h f.qhkuuw:78jbtlfhe8g. 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 rotations in 1.5 s when in the tuck position, what is 8 hhhl m*8q:uwf b u*06ftjoeke.s97x her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rs-qzd-cfti80qjud(y6 vw,bxq.:5 nl n m,o e6otation rate from an initial rate of 1.0 rev every 2.0 s to a final rat -fz8nq diq6wml0:vou-yq b e x5,n.t,6cdjs(e 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 throughy1a9 y,t z-sst 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 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the cenz,t -9sya1y tster of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular zn4t, jm ,v w*tapb6p8momentum 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 momentum of the 5/ ea+jp-c:rc3 jkez /apdy7gEarth
(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 inertia2ml cigc* 4 opkk p323kf-.obn I is dropped onto an identical disk r2kio.f* cc-k2b gp3nom4p 3kl otating 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.m3 brry.j2 bj:-o2r- dwf (qff4 $rev/s$ 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 p oyh+2pw 6ml t(gqu t*d89wy+a rotating merry-go-round platform of radius 3.0 m and moment of inertia 9q ptl96y*2u dgwmowp y(h++8t 20 $kg \cdot m^2$ 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 fre9bqt6j1xgi ql /croj5yb 3 x6:ely with an angular velocity of 0.8 ob/l 63j 19xiyq:cg6qb tjxr 5$rad/s$ 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 collaps 6 wp1iea o8/af/twl+qes into a white dwarf, losing about half its mass iwi ae6lof 1apwq +/t8/n 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 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 120 rx(tbp)urc( /,*d+ i ewgdj5m$km/h$ 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 jvaa:()wr cle7oqv 10$ 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, initiafs7m 6r+oqq, jts9qy8bw3h7 flly at rest, that can rotate freely without friction. The moment of inertia of 93j f7qyr +7 86s mbqsh,qfotwthe 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 stands at the edf;t c3dw ;cqd.m3s) pjge of a 6.5-m diameter merry-go-round turntable that is mound mjw.d3ccst;; q)3f pted 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 grounh)ka, w9ihyupzv7 gb.3p.y-md-e m v,d with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool ro bph,y wkegapmz 9yvu3i- v),.hm d.-7lls 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 s /fwj:5 tne*xguch that the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle oen/*wf5t g:x jrbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at ahp t2jx z uy2e-n,,r+b 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 s5 l*qhcu;.kza-cl6,2 agtu sm acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the ;-*,tgc2zhslkal u6s q5a.u ctorque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical dis--vm7k uzh6mb ks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mbk7h-m-u zv6 mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is lfsvz tis*;q::g rs (ctz+o18the angular speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 times as great, were rotat )/nw+lbk**bmbqpt sy+3q+cm4n) nln(f gif ,ing 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 the4+q )sfwf*cy3ngqnbbln +p lt *,i)bn / m(km+ 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 automlpuc)a4 u .;;7q moghtobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 muumh.p qc7ol;g4ta); 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 illustra:3f9 tbt.dzw stes an $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizont; .f/kit)c-at su 6zxjal 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,2 5 -bymhyll5nz alc1., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the -y l5nb ml1a,h cl5y2zrod. 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 vertically on the floor, and fg7o:d 7l ywx1we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step has height h, ww xl 7of7dgy:1here h

  A bicyclist traveling with speed v=4.2m/s on a fl96 wgvqy)r y*v ag/f8oat road is making a turn with a radius The forces actinf 98vq)oa /yg6rvgy*w g 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-k4 ah7u 6hfd1z(ox l- fdqsv9k0g rock into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head,d afvf0 uhq-okx46dzsh(l79 1 accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thin rods, mndebz-uu9. 2 making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arbem2 n.9 -zudums, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical plad:b(duir-(dd*n kfta: fc0h0 c+q-kk tes, of aktc dk idh (-cdk:u0q( b+:0 d*-ffrnmass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 roll.3c1jnvo/q) w wds :q7ush)kf s along the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the )cws. q1:jv73ku nqfso)/ wh dmarble must drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assume z)j;9gf5blulr*f vf8baa0 .4qf.nm k $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the caq ql1:a0k qr( od4ae;sr reduces its speed uniformly frqq0ldes 4qr( :aoa;k 1om 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s