A bicycle odometer (which measures distance travel1 th 4 vt h)xqg,cinm(f1.o//4r jaakyed) is attached near the wheel hub 4 hxcr1a )fva4tgknt m. y,/h(1jiq/oand 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 nrou 5z:p .lms-0b g/69jpxctpoint 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? Foro 9m/urz g-5s:ppbj0nct.x6 l which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be describ mrj+9qsv0es. kudije+ ,. wc9ed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a large5cv ,6r 9xh*e 8nb ozly1b)iker 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 h(nhr.f/h ,c xgd1mhj2 ands behind your head than when your ar.hhhj/(n1m,xc2 grf dms are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven in+8n9btz d2vpi s)q oe12, uasprockets 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 gear is it harder to pedal, a small front sprocket or a laru12b, v)itizd pq 8s+n29oan ege front sprocket? Why?

Mammals that depend on being able to run fast have sleg 0d+ik4v2cffag- w(2;cy cr 7wrads6nder lower legs with flesh and m4fgwvcg2w+ad;ad6c y f srk 02r i7-(cuscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, nar(ree;l 3+i fdorow beam?

If the net force on a sycu d5qec7doy9o +1g01v pbot3stem is zero, is the net torque also zero? If the net torque on oyc57o9oce1+1dut30 g vd qbpa system is zero, is the net force zero?

Two inclines have the same height but make different ;w+q i irtb839yrk*x uangles with the horizontal. The same steel balwtuiqy ; r*bri83xk9+l is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) dowb7jwq9lj m(yl8*j., q,gxc i in an incline. One sphere has twice the radius andwg qxib9.,ly8lq* j im,j7 (jc 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:q:wqu v --ith same mass. They start from rest at the top of tiu: -hvq-:qw 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 mp rxf4b6)*afqomentum are conserved. Yet most moving or rotating objects eventually slow down and stop. Explaif p*bqxfr46a) n.

If there were a great migration of people t/*ibw we)ix m/oward the Earth’s equator, how would this affect*m)ex /bwi iw/ the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any initial r1:cekrjmg 9 ijoqzc* 0*( rzbq.l(/ aqotation when she gqqjclrjb*k./1 i0*oq rm:9 (eacz z(leaves the board?

The moment of inertia of a rotating solid disk about an axi c/o7 zpuqy*6-lx,nobs through its center of mas*nlu,pqx 6 bzyo/7- ocs is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holding a 2-kg mass itivj7;ti+ oh-n each outstretched hand. If yohij-+tt v 7;iou suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the samejdj k *h35scq0 mass. However, one is hollow and the other is solid. Describe an experiment to determine wh*kc hdj 3qs50jich is which.

The angular velocity of a wheel rotating on a horizontal axle0iapdfm p8ee8f6:-q8iy2b 4xn :zsa y 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 poimna-08bpqy4f :pxsz8:eied6 y a8 f2int at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rojca, 4.dbp+ hhtating turntable. What happens if you walk towa b h4+d.,pchajrd the center?

A shortstop may leap into txdak o/ *,exs*0t;3 w;rjn5xubkfpi/he air to catch a ball and throw it quickly. As he throws the ball, the upper part of 3 u d5nteor,//jsp* i;;0fkb*xwx xa khis 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, discusm3(c ,i * b dyyu3hb.5hp5woxcs why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the seyhuhy.dp,bc3 * w3cxo5m (5bicond propeller can operate to keep the helicopter stable.

  Express the following angles in radians: (a) y(dr r 12lhq g7cpz-.y30 $^{\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 coinciden*gk k t4zm6ht2ce. Calculate, using the information inside the Frohktt z42mk6g*nt Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directc9r6fi npg.q+6i8hub ed at the Moon, 380,000 km from Earth. The beam diverges at an hn89fr.g cp+q i6u6ibangle $\theta$ (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 aj ms y8iy+x* 8pi,tac/t a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What+p c y8/*i xiasjm,ty8 is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a qjrs0zmh9c 1q rk2;wl+ht2u: level floor 3.5 m to another child. If the ball makes 15.0 revolutionsw1rhtrz; 09km squ:cjhq 2+ l2, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0, *+t* wje.d lqyw3u zjx/y/sk km. How many revolutions do thet*.xuj+,d/ j/w zl3eksqyyw* wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rph)mg ,))vd0+j*vdwv1atwxi x m. Calculate its angular velocity a *h+ vdi1mx0vwg ))jvxtdw,) 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-rour;m)z fu84zz hnd makes one complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seatedzzrm;8h4) zf u 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 t3j7)v fxdp2r7i- zk qvelocity 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 spee g nd/ypsc)atx,b3ltyea::.9 qxv ,b2d 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 frodeo py3* .je-dx 9j88moo 0dttm the axis of rotation is to exxj y8m08e* de-d. dpto3oto9jperience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel ac o7:gsk.s)1nu:qwl kv:t0xuf(jzcw6 celerates uniformly about its center from 130 rpm to 280 rpm in0:wnxwj 1 zqfvkk usc o:)u gs6:t.(l7 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 radius grt2xo:uowb+ *e4p bvn jb;rqp,: +r($R_1$ 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 Mooib6 u 0ut4z3hun, astronauts aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12u0 6ub4z uht3i-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 unf9 hql ojsdzpr;2j/-+ iformly from rest to 15,000 rpm in 220 s. Through how many revolutions did it tur29q-/l;hfzd+srop jj n in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rdbdm5mcp58 l 0pm 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 dr* sa0 stz: t39s-si j yuz;vo*-tot0b1k; imfor the stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 comzu*t;-;idjs09 yt -o*m1 at:tv iross3zs0k bplete 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 acceleratesv+y5 ( r8/ uuqy/vjo/i+lebhhfo x2c: uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on thovuv /f/o8+2 x +yjqh he:yrc(bu5l/i e edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turn8 snmrtw*h/yoc62 eo3m 67iwrs 1500 revolutions before itm 76 mho *2/ceon3r8si6trwwy 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 m5j sq j4mp6l/i-,pxq wake 65 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tire p qsp6w4-xjmlq/,ij5s 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 revoluti5 *h0hclk2m h stu-0ktebs-2 fons as the car reduces its speed uniformly from 955kbthks *us0m c0h2-2t -hfe lkm/h to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on each pedah9 i v +arf97aceeaa).l when climbing a hill. The pedals rotate in a circl)reh fci.av+a9ae7a 9e 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 :)+ k g(leitbeqko/b4t2updfu. ;4wh 74 cm wide. What is the magnitude of the tpkukehbl f+iwe(o/t: . qt 4;u4b) d2gorque 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 *o5i9d8 mf du xs7+gefaxle of the wheel shown in Fig. 8–39. Assume that a friction toriso8ued7gf95* dfx m +que of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of masss;1twyg3+f +, vezij bhrowe;5,gx 5a m, are attached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculata3xz+ge1by fsrw tovi+g;5eh; 5, ,wje the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tigh4l;z;pdoyseu(p8. e )vjp. pai0aszlk9 v g 56tening to a torque of 38 .e4;8lss0;v)6pp py l5 dkju 9vopag.zize(a$m \cdot N$ 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;nzhtf- -l rj*)xe5 ts m when the axis of rotation is through it )hex-l- ftjr5s*z;n ts center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicxp ck+h2.x;w s3 s0aamycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can b. hasxwx kap;+2sm c30e ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, ligh3yh hmh*)w,p/d9yxvu t rod is rotated in a horizontal circle of radius 1.m 9 )*yyx3phh/wh,vdu2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rotatinh/x k-k.w /i)5lnjyp ng at constant angular speed (Fig. 8–42). The friction force betweenph )x/nywn /ki.k l5-j 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 td z q7xgh(34g 4oic-v/ dpki 2e3y7jerhe array of point objects shown in Fig. 8–43 dh e2(zx-ocekigg437q d i v3j47y/pr about
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxw*s.7ntzon2z eg7v-b ygen 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 cylitl cfzi/1hb *xh51fu m 7o:cl1ndrical satellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44mub1 o1c f1/*hl l5ztx:h7cif . 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 and a p, a dbu)v:1 duqq15xomass of 0.580 kg. bo1,dx1a :uud)qp5 vq 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, acceljf1 tdju2u8:u erating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-driven merry-go-round and ifjzqn0y2-:ma/: hkvd s 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 chilhkfay2/d :-mvq0 n:zjdren (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 rotating at 10,3,10b-ofq()az8wy*hp d*y+kldinv me 00 rpm is shut off and is eventually brought uniformly to rest by a frictional torque e-,nbdqvyz(wdfai+1 p 0o *lk)*8myhof 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a 3.6-kg b za7v, wu*4xgsvj3 0g:psvrq-kg d 0s2c*jm5v all 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 ack69scgu 0gbw ;tion of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly fcsg b9w0g6u k;rom 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 bw6 xu 6j*qd(eopjwe. ;(i ed0clade can be considered a long thin rod, as shown in Fig. 8–46(w j;e*j6(6cpiuq0e x wd.ed o.
(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, q95tx/y 2xqwx $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest wiw pa* ;fe:ilyr hdz0 0epu(,i7thin four full turns (revolutions) anaydpeuz7w* :i r,e0 p(f0l i;hd 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 inertia3z0,ekm c+b nj*la )i1 qra7ba 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 develop5 d6v gzda-ydc+ .6mmna :qib721)3higjjq iu s 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 rolls without slipping down a lae)s dn7qy( wn0ne a)0s7ed n qyw(nt 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with rxc;l+,8vxwtsl j x8k0 espect to the Sun as the sum of tlvx xjct+;,x880wk lswo 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 ww;:q( wvk+swax (-armass of 1640 kg and a radius of 7.50 m. How much net work is required to accelerate i:a akx-+w srv (w;w(wqt 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 fr;blwnc r n+vzn19:c gf77 s1starts from rest and rolls without slipping down a 30 l w7cf1z9c1v:rf+7nbn r;n gs.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 bx9tp,rf h0 b5ualanced 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 hits the ground? [Hint: U9ruh tbfp0, 5xse conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the end of a thin st6+k cx kshvrdjx (7b,j7)( aedrings7cd7jj +)ab ke( rx(,x 6khdv in a circle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-ka;z3n4*)kyd-bikklq7 3ew twg uniform cylindrical grinding wheel of twq7ik e ;*bl)ynkw-4dkza3 3radius 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 platform that is rotating asa )b 0n,b2ds no/)7s*dfq ztn 9vgyy4t a rate of 1.3rev/s If he raise 7 sndny,s/2a4 )zs9tdn*) vqg bbfoy0s his arms to a horizontal position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fx d-d qc4)pf;0bnem4 zig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing f ncxfdz-4)d0;4 bempq rom 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 increase her spin rotation rate8: 9i t*fklhv(p(gmrbz -ye r) from an initial rate of 1.0 rev every 2.0 s fph( zlykib-*(rm9t :rg)e8 vto 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 rota c2tigpi1h(oo5jz6kisr ,ia k-q 095pting around a vertical axis through its center at a frequency of 1.5rev/s The wheel can be conside tp5aj( chio-gs56q1riiz90o kp 2ki,red a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skc 4 kih kw,5w fr.xds;jt7a1+hater 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 oft,ymgz xzy 5 )k2 *nso.e+ytb5 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 cylindrical9v,rsxj 7 r-3ek-jqj7o*mdc n disk of moment of inertia I is dropped onto an identical disk rotating at m vrc 9nrjs 73jq,*7k-e- oxjdangular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.jhq+b 9y6xy ;e9f*-mjbt4kqb 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 a9 *wyas 1lpo)kg stands at the center of a rotating merry-go-round platform of radius 3.0 m and momenta9as1 o)ypw*l of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely with an angular velocij;gff)s or)k) ty of 0. )gr )s;k)fofj8 $rad/s$ 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 abdk q)umumrv x 5jxfir/ /1u1xu9** et;out half its mass in the process, and winding up with a radius 1.0% ojm rr //x du;1e*xuiq9) kt51xfmuuv* f 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 ingjtdy/*qu6hpn.h63p+7jgf6 i kbqy4 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 9hf .qw2cme ;f,1z fkg$ 1.0\times10^{ 5}$ traveling at a speed of relative to the Earth, hits the Earth at the equator tangentially, and in the direction of Earth’s rotation. Use angular momentum to estimate the percent change in the angular speed of the Earth as a result of the collision.    $\times10^{-16 }$ %

A person stands on a platform, initially at rest, that can rotate freely witnip s(rz1:dq(hout friction. The momenq r1pdsz: in((t 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 s;i cif99k1 whj:c tr+vtands at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of inertia of 17jc +:twrv9 9;hck if1i00 $kg \cdot m^2$ 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 rope*-yaa em cf87/hidw x3/f7z hj 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 ai* hhax7 -m/cey78wdf3jf / zperson without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side alwgpqma(i 11ek .ays 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 orbiting m p.(1gi1qa ekthe Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate hb43zsy r7i5cof 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 s,-j5uw2 kw/zs xrf4b 0g6kpbn2 kv.ze hape of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at cw-vsb0w2unb efrk4.j 5k zg 6x zp,2/konstant 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 0.05 du4hcgi2 +4kn0 kg and diameter 0.075 m, joined by a (concenh4i+k c dngu42tric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it 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, honsyf 1khwkf,: r dwofx4**t+9.ttun*w is the 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 greatp h9yf9p fqq9 w18sa2p, were rotating at a spepfqqa99 p 1hf 28p9yswed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to uq qra dj9*s.k*/kkui 4se energy stored in a heavy rotating flywheel. Suppose such a**/qi.4 r s9kkuad jkq 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 ;1-se-w-lu0ypr4y vvdzlpeb 45oplqdh06 t; 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 *pfxdmgz kcs+z-yw a/4 j-py40pnh+: surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (i.e., we ignovv8oi6m ei82lre 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 e68v2lv oim8 iacceleration 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 +. gd3e:ph7p shhd lq/R. It is standing vertically on the floor, and we want to exert a horizontal force F at its ed+:g. / dlhpq3shhp7 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 o6ly 9rs5sr6)a7(zbt t /eeb-oacw h(is making a turn with a ra9 b zyw(tlc b5ra)ra ts- s6ee/(ho67odius 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-k9ta *5f+kmkak)c,z4m qblg 5 cg rock into a sling of length 1.5 m and begins whirling the rock in a nearly horizonmfc),k5k4mcg+bl 9z5 k ataq* tal circle above his 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’sa.; u+ 8tan bhcq4k)rion9kw, body as a solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then cacu,n8a noak w; 4h r+.k)qt9iblculate 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 whics3yvj ,1j0 tbyk+in5jyc04jj h consists of two cylindrical plates, of maj3j syibvy4+nyj1j, 0c0t j 5kss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 radiny5djm :i -sqcg07oo +us r rolls along the 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 reach the highest point of the loop wi: cjo-+g75sy0ni dq mothout leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do notmjit.lxyx )4puee9/ 7is/j+ u assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces i2-bam 2do g;fpl.r::k 4vlrsits speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m.r :. mvrk: ofdl42a2bslpg;i - (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