A bicycle odometer (which measures distance traveled) is attached near the wheel+02bvxvraql kwg 72l6 hub and is designed for 27-inch wheewvbr2 kg a07lv qlx2+6ls. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a poinhh:2sk f8o i k7dto--zt on the rim have radial and/or tangential acceleration? 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 8to2ok-h: hdsi 7f- kzacceleration change?

Could a nonrigid body be described by a singlezd 4.7j20jkeyv nixox wf5r)w1 :hr*l value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater j7cvmx 2 nt4u5torque 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 hands behind your h+)i 0xvwavf. head than when your arms are stretched out in front of you? iv+)fw 0 v.hxaA diagram may help you to answer this.

A 21-speed bicycle has seven 23 jz5 h,fdzh/gpshu 4sprockets at the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gearf24 z u5/gd,jhp3h zsh is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being abl ohk8mwzr r zu z3nr98,5m0t6ee to run fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 6r 3mo8umh9,rz5zrte8 k zn0w8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long zib 5,)s-ykop, narrow beam?

If the net force on a system is zero, is the nmt.; b+u,zppx(usbq 1t4rg w)et torque also zero? If the net torque on a system is zerxgt (pw4m1 ;+ tq)z.bp,usrbuo, is the net force zero?

Two inclines have the sact q i9wu(3wb-me height but make different angles with the horizontal. The same steel bal9bct3-q(uw wil is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (fro 3dvuo3iooj8m5q 5g-c m rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of tuood85jqvgi c 3 3m5-ohe 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 s27 lh7wn;ia n0zouxfqfh/6 8bame radius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has theq 6 ubf oi2a7nx/hw;8f hz0l7n greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most moving or p0bn 9nha:c3 nrotating objects eventually slow down and stop. Explaia:0bp3 n9 chnnn.

If there were a great migration of peoplei.nxhf9n n.,h toward the Earth’s equator, how would this affehxn,9nfi n.h.ct the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any initial rotv3i )3 k(dw ca0gygw*3gy0ee .vu fba-ation when she leave.a*v3g3 uw)yw fg -ie0 (b0gaed yc3vks the board?

The moment of inertia of a rotating solid disk about an axis through ig2khh,)*pskot kos1h1ml:l : ts center of mass is1k): ohlhkt*gpk1om,s h2:ls $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holding a 2-kg mass in each outrmtie ,wd9r:* stretched hand. If you suddenly drop the masses, will your angular velocity wid,em 9 trr*:increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, ons ..+xyuy6i o,x twvr;e is hollow and the other is solid. Describe an experiment to determine which is whiwxy+i t.u6or ,. ;vsxych.

The angular velocity of a yonprr2 6*. aewheel rotating on a horizontal axle points west. In what direction is the linear velpar *2reo6yn .ocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edgey+vbh9/ kyt7d)x/hfo;4et jc of a large freely rotating turntable. What happens if you walk toward t/h kd7y)tfhc;x t9b /joye+ 4vhe center?

A shortstop may leap into the air to catch a ball an j5gn8z 9 fepwm;pb4x*d throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you 4nmejf9z*;5p8 x bpwgwill notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law: :mph*dwpfd5,n 2tc gcai 3r; of conservation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.apprc*w2,:;fd5t3:nh i dc mg

  Express the following angles ia e1o2e+ +lht9,b+dj u 8urfgtn radians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coincidence. Calculatezu-id.b ;,2fjhv m) kv, using the information inside the Front Cover, the angular diameters (in radians) of2m;hdb j-kzvi, uf).v 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 Eq rcej x gs/dgl 89xg+.8z+ek+arth. The beam diverges at an angle z8+s/xe. e c+gg k +d8q9jlgxr$\theta$ (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 v5 5lc.tqw7 )7:qx8cj xhyvwy a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades cht)cxw:5xy87 q v57w. jqlyvslow down?    $rad/s^2$

  A child rolls a ball on a level flq4 , 3:9 )tpahg+fpiiyy (fjnuoor 3.5 m to another child. If the ball makes 15.0 rev aq 3 fit4yh)pf+(giuny,9p:jolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travelsxs1elmww5(,z ; d mjm/ 8.0 km. How many revolutions do the wheels ma e;, lj/mw(5wxdms1z mke?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates /44pd n(zu; 3o ae4w6thfioroat 2500 rpm. Calculate its angulnu( ht3/a weop4f4;r zod64oiar velocity 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 8-i y-s. ;fi xi3rjlcxrevolution in 4.0 s (Fig. 8–38). (a) What is the lineax-f-8.xl iiy ;rj3csi r speed of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) inpcskd x as)oi 0a:7:/y its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a hk)r c:hbkb .sq0m5a3point
(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 partikf(hxf,t+ /)kyp hp /fcle 7.0 cm from the axis of rotation is to experience an)+(fkkhtppyxhf/f , / acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpm to 2s(0xng cwz q74 g3vy)v6nhu6 x80 rpm in 4.0cnh nvy3 gqxxu)vsw67(6g 04 z 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 radiua9ht6aa9,74)lv efgi4r jqex s $R_1$ 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 spacec)w i,ur x53rh v6sr2cwraft 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)r ww5 rir36hcsu,2xv 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 unifo4 bzbv-ih o+, wq2odu3rmly from rest to 15,000 rpm in 220 s. Through how many revolutions did it turn in this time? 3 -budowovb4q,iz2 +h    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm inokmh psfk0a00 82mbp t ua;q+9 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jets in0a6q xd od((nn a whirling “human cennn0 oq(6(ad dxtrifuge,” 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 a g ,wfe0amlzyc-8.+7bca3 .4im kmxzoccelerates uniformly from 240 rpm to 360 rpm in 6.5 s. wzc - 3kmm z cl,f84eobxma.. +aiyg70How far 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/ 92koo ouwn9mgml k8*zxw 47;ymin It turns 1500 revolutions before it comes to a stopyxw2m4 klgz98o mo;*won79uk .
(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 cr, o+(svo8p+ mjys ckjqe*/u ;ar reduces its speed uniformly from 95km/h to 45km/h The tires have a diameormj 8qp j,uosecs* v/+;y+ (kter 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 mn dl ym +d(zhw,2t*f1rake 65 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.w y1*d(rznl thd2f+m,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 afh-1 -g,m pfvb14ps0p sis sn.x2rlx 4ll her weight on each pedal when climbing a hill. The pedals rotate in a circle of radius 17 lm24. vnr1shp pp4sf-xi ,-sbx1f0gs 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 i+ 128 yi ltwfu1jlr:/dm2+rcsprbh8on the end of a door 74 cm wide. What is the magnitude of the torque if the forcetirh 12 drc2/1 irmw8 8sjp l+ufy:lb+ is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel shown in Fig. 8–390 oa,g 6v 6ng 6*p5)3csj lq*xdgkudie. Assume that aq0k3 ing,asp) gd66ov *uelgj56cd * x 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 attar11t euxiqm17cv 0nq)ched to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in th7n1c0xi 11mrq)e uqvte 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 ksu epjlb6 pug;s- i-.rl *h+1ajov:7 tightening to a torque of 38 aek jpu-l r; h ui6jg-:sl.vpso17* b+$m \cdot N$ 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 0.64u3mobreq5 7t88 m when the axis of rotation 3r t7e85oumqb is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle w* w2gh34y cw3udf wk0.ox qqh26l tl8qheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. Thkgfq23 llwqdh.83 w 6oc*qx0wtu4yh 2e mass 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 rajq19wg nsr*1ip5f-9 j yl8v potated in a horizontal circle of *1lprv jsip-n 9 aj95gfy8 qw1radius 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 bowhw 6uqv; rdn d*xc0;:w 37cgvpl on a potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and tc;*x3hv0 dd;c 6v:pwurng7w qhe 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 aq8n 1q )4ehmkpcc* :hjrray of point objects shown in Fig. 8–43 a hep)k4 j qc:1qnm8hc*bout
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxygen atoms whose total ma h25mm)pm+2lgmvn- cg:(e- prm aa8ux ss 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 spijqv h rq igq+1a 1u0.op-7b2frnning 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 reqa r+q gq7p oujrhf .bi1q-v201uired 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 and a mass ofo,d5 j 1alilcbe+e+ x;wh7*ha 0.580 kg.w*ha,7l+ e ;ce5o hbxljda 1+i 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 itw b9pik ryk/ht yg5v 2oa;,vjiu;8*l- 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 s6km rhn4ftga/9epk9 3lbjn9 7mall 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 each other on the edge. Calculate the torque required to produce the acceleration, neglecting f49k6r amf jnnetl39g/h 7p bk9rictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 )a e3c k7daof/rpm is shut off and is eventually brought uniformlf3dae/cok)7 ay to rest by a frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 acceleratehpetd ;d1 +3xls 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 the forearm, whigf4p/rt oim .dcmluk8k4c3 +2ch rotates about the elbow joi / k ilp82m 3rcdtc+umg44ko.fnt 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 a long thin r5 wd(mcz,vzmm/.5imqt , (.ml 0xxs8lxtlb*iod, as shown in Fig. 8–46mx i .m0cxq(8d.bi,t5,tzl(mlx v5 z/w s ml*m.
(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 consky :+ 7cv4bgzgists of two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the h+,h aytiv 3asgt7+c978pk ljam u. qh.ammer from rest within four full turns (revolutions) and releases it at a sm sa+8quc9hy, .hk.l7jpv 7g3a+ it atpeed 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 momenih6p l3ypjlm*xf/71i t 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 ax vw8a2j-rr5zkm 71u(s ffc-f torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls without slipping down cu y25 n-kf0ada lane at 3.3 -yd ku2fn0ca5 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of theeyn8xe-(kzt8mk uqmnk m(. *+ jkw5 ::tuz 7ya Earth with respect to the Sun as the sum of tw(e*.nnk 8 7+kzym yut-ekxq m(:m8k z5u wajt:o 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 ofysac 7*6sj9)q.vx peg 1640 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a reyqjsgs.v *6p 7a c9x)otation 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 fro.t2bap v 1kzo.rq *w9cm rest and rolls without slipping 2r9czob 1avpt.wk *q.down a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

  Two masses, $m_1$ = 18 kg and $m_2$ = 26.5 kg are connected by a rope that hangs over a pulley (as in Fig. 8–47). The pulley is a uniform cylinder of radius 0.260 m and mass 7.50 kg. Initially, is on the ground and $m_2$ rests 3.00 m above the ground. If the system is now released, use conservation of energy to determine the speed of $m_2$ just before it strikes the ground. Assume the pulley is frictionless.    $m/s$

  A 2.30-m-long pole is balanced vertically on its tip. It starts to fall and itsdns)jp6 -rh(z7,f.sk j 7zzux lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint kpj(6d7zuhrj, .sf)z ns7-zx: Use conservation of energy.]    $m/s$

  What is the angular momentum o( 5hw5fu eyfahnz s:.,azh3 .of a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an angular speed (5sao z3ewha,fhyu z5 :. hfn.of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momenjb2ing-qwonipfo l8 r88*s, )tum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cmb )ooq sig 8n8w*n 2rpfjl8-,i when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that is rotating at a ratc(g h*z x(hia )-uivg.e of 1.3rev/s If he raises hic)(ha zxgghu(*-v ii. s 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 sgrxlt1 a:p)hs;x/gn u -vm5 b+ff 6q7bhown 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 rotations in 1.5 s when in the tuck positi txg:g umq6nb1fp f-+r s )lvah5b;x/7on, 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 qd;)8tnh :pdc of 1.0 rev every 2.0 s to pht:nd) d;q8c 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 rotatingj,le yf,pk 2 5fzh 8y9w6 sul./fsz3rqp8u .nn around a vertical axis through its center at a frequency of 1.5rev/s The wheel can be ur5yzp,f36 uf w ,zy9.8. e 2qlhjfn pkns/sl8considered 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 angudqjtp8n4 c+s 1lar momentum 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 jsr9t +-4l aoa+x.v)q;qz.qg uhurt 2 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 mup dp+zk a8 z+yj+fye/(.s0fI is dropped onto an identical disk ro ydkm+fzj.e+s/(p u y +a08zfptating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turnsc qnxhz)x e 4fl3-)s77* tlawu 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 a rotating merry-go-round platfiy6 +ka+qhva v 4f7lul4yt8e-orm ofl-vay4qva6keu+ 74hyi t8fl+ radius 3.0 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 g) rg47mtqj8wqgd7iw d* pt29 an angular velocity of 0.8 * 8 gqrtw7d7mq)4wj2g9idpg t $rad/s$ 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 coo5pp h*d(qg e/llapses into a white dwarf, losing about half its mass in the process, and winding up with pegq oh5d(*/pa 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 w ol z6 let;0w19y yy,ajsryv.-inds 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 a,9 w0zsnp-)rqoa. v: ycg2pv $ 1.0\times10^{ 5}$ traveling at a speed of relative to the Earth, hits the Earth at the equator tangentially, and in the direction of Earth’s rotation. Use angular momentum to estimate the percent change in the angular speed of the Earth as a result of the collision.    $\times10^{-16 }$ %

A person stands on a platform, initially at rest, that can rotate fre:)fngitker 28 wabqt hs))l8,ely without friction. The moment qwa 8 rl)eb8),nfit s2:kght )of inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of aev 1u9)trqk +r 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of19+qtvrkue r) 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 ground with the end of the 5jtpnkt2tz95 o+u 6wy rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind5twknp tyt 926z o+5uj 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 Ea t4thz2;dgq 3trth such 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 particlet43 t htdqgz;2 orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of ve6iflp tzfe1(* / q* 3to0hsa1 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 sham ll7f7yf1-afpyj a(nw*26eu pe of a uniform cylinder of radius 0.20 m acquires a rotational rate of f-7yjaaefpu7 fl2(n *l f 6m1ywrom 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 0.050 kg qv w i521;(hxix7 nikhand 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 enerhx hiq2kw5;iinv17x(gy 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 t v+it 0mgiw;ix78jet r8djle( 8f8bz ;he 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, butlryh o6j4e)on xv yh gv,9b.bqp05)5 n with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every, bhnej 6qyp hnb45x5y.)vvogro0) 9l 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use energy storedd7 . /xeit;iud in a heavy rotating flywheel. Suppose such a car has a total mass of 140t/x.;7ei duid 0 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 illustrateipf-egbk5*k * mi rt+;s an $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizontal surfac 13ogl yr5s,q.,lwwff.nd ;xq:bn +cue 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 l0c gu2a heclqr h6mj a.,,+4gfreely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the liaa.l 2mgghlh,qc 4eu+06r,c jnear 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 raqqs.v; uagd l353nslk8p fl35 dius R. It is standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will cl3 l3pslgnfkqla ;d3v. 8q5u5simb 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 maki0e; -l,eyylm hng a turn with a radius The forces acting on the cyclist and cycle are the norm0;lm,hyyl ee- al 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 kujkb7c4: aw q ;:gqy3i8cy4orock into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above hiqkq i g4cyk:;j3a 4ocuywb87:s head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body zhs/p5 pb,fg8 as a solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratgp p,z 8h/sf5bio 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 con32mwy1a(*;bes2kgbj ex,i q( rder.o sists of two cylindrical plates, of mas.1ex(a(qeb3j2i ymdo w2r*bk egr, s;s $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 x,f xw-rr8 6v 5w(4 hs +9aunnrpjfi-q44w biolooped 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 reach the highest point of the loop without leaving thei-haroxb-q5u+nx44 vp w8f4wn sif,6 jrrw (9 track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not asezvvrgpy 8 p 0g8n-z8k *ghc-/sume $r\ll R$ h =    (R-r)

  The tires of a car make 85 re 9h9 vw-yx9hgsvolutions as 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 angula shg9 hw9-9vyxr 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