A bicycle odometer (which measures distance traveled) is atkp/b/ph ;4epi tached near the wheel hub andp/iepkpb; 4h / 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. D zx, x2h ydr9k.m+ly( :qvijz6oes a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radialdz9x 6mv: q.yk rjlz(,h+y2xi and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be describe c+15t rxek6tswh1:nfd by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Explcbjp8 cg5:3abain.

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 lbp7krz/ifxt 1-* n *kto do a sit-up with your hands behind your head than when your arms are stretched out in front of you?i-tb r lx71k p/nkf**z A diagram may help you to answer this.

A 21-speed bicycle has sene rbct +x)6*9evc,dng8wbuc5h /m(hven sprockets 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 *nhcwg8rc ,h 6/d+ xbcuv(m)e9et n b5large front sprocket? Why?

Mammals that depend on being able to run f inz6ec1:1 oiyast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantag:e 1c i1yni6zoeous.

Why do tightrope walkers (Fig. 8–35) carry a long, nkt9ip)hn x6s8-h 8g ysarrow beam?

If the net force on a system is zero, is the net torque also zero?jpd l5v qo.1c( If the net torque on a system is zero, is the net forco5vl(p cq1.jd e zero?

Two inclines have the same height but make differfm5 jbjz//rl1v 4yiv6 ent angles with the horizontal. The same steel bb/ yv4rj/zl5f m1vi6jall 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 rollc2dauxph ot9s5fvxm)obpk+ *y ;7r5:ing (from rest) down an incline. One sphe92ft:p) yx bm5rsxcu ;ov h*k5p+7oadre has 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 mass. They start fr5pl v0 +f6kndi:kp-uw55mip3c v ixg0 om rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy a3if gu55wvp lm -:kcdpkxpiv+50n0i 6t the bottom? Which has the greater rotational KE?

We claim that momentum:vgo;d1lvk3n,+hxvs2 )7qgv3 hau md and angular momentum are conserved. Yet most moving or rotating objects eventually slow down and sto mh12 x3)ua,ohgvv 3dgl+;ns qvd:vk7p. Explain.

If there were a great migration of people tcjfj .dn l)33 p1bspeaf; .mn-oward the Earth’s equator, how would this affect the length of the day?1d;fcb 33lajn- n jes.)f.p pm

Can the diver of Fig. 8–29 do a somx x0uc6 +wpv6x3.fd caersault without having any initial rotation when she leav6a cxd wcfx v60p.3xu+es the board?

The moment of inertia of a rotating solid disk about an axis t-e-8bdz1t afphrough its center of mass ie t- fza8-1bpds $\frac{1}{2}WR^2$ (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 .3wu/jvu. -deo;mkzfmn p a,g5sq7z8 in each outstretn,u8fdm wesk-zgq7u;j.3 5/mpz . avoched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look idenvyr :6xvuwhyl n+p*jp( q1j-2 tical and have the same mass. However, one is hollow and th(pvx2ryq1lw:uhj6*+ - v njype other is solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle points west.p pyw84,wzgg1qyhbh- lj00c u6* njw3 In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangenti 0w,-g8 n* h3gybcqwl ywpz61jj p4h0ual linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating turntab.my81m76j(f ix2jjfdl 3 yqeple. What happens if you walk toward jfd pq xi8f21 (6 y.jyem37jlmthe center?

A shortstop may leap into the air to catch a b )cr v.1 viq1ed5d;im6v5t9gd )bso qvall and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. v)cdmq5bvi1 .d1;d)go6 t iqs9e5rv v8–36). Explain.

On the basis of the law of conservation of angular momentum, discuss why a helqyqpzmsns1b- w9. z60icopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to kee-1pbz9yzsnqw 60msq . p the helicopter stable.

  Express the following angles in r,o 66bhnxs2l dmpi6o/ adians: (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 b 4dq/x(qe-9zs ymvx,pecause of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as -qmx(s,4ez qdy9vp/x seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam diveksa h2)4o,uqk xb95ryrges at an angle qh,xrb2 y45 ousa9k) k$\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 r27n:vmqi*mh*e f.seppm. When the motor is turned off dur .ee vf*m*i:h2nps7qm ing operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If the bal1in cir;35lezj: v2vp(y0yhz l makes 15.0 revolutions, what is its diameter? z1 :n 0v2er 5i3jp(yyh;civ lz   m

  A bicycle with tires 68 cm in diauagn b 21bhf5 h./-kofmeter travels 8.0 km. How many revolutions do the wheels make/g-.ak bofb1n2h5 fuh?    $rev$

  (a) A grinding wheel 0.35 my qp) ym(j. ak(o78ubrb,1xgc in diameter rotates at 2500 rpm. Calculate its angular velocity i., (xb gc8 op yykjbam(q)17urn $rad/s$ $\omega$ =    $rad/sec$
(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:we n-u8agaih b(anrzr g) 0)h i99fi9 (Fig. 8–38). (a) What aigi8g)r w (ua bh9f9n)-nraz:he 9i0is the linear 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) in i w283rjyo :6w jq3soznvwwa0 /ts orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed ou2w /2 zk-gojnuv,/:8owog u hf 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 7.4eid7r ph7qg .0 cm from the axis of rotation is to experience an acceleration of 10p.4d7 rhiqe 7g0,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpm toimnev5 )kw+y 1 lu)ke3 280 rpm in 4.0 s. Determei)yu k)3n1 +le5vwmk ine
(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 radiusep xsvxnt/0 uaq4r97 (sq)jb. $R_1$ 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, astron0ul g4sco -b;kauts 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 12-min time interval. The spacecraft can be thought of as a cylinder k0 bul;- o4gcswith a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,4 eetq2i0-y jm k(8ieg000 rpm in 220 s. Through how manmj20 k4-tig eqe8ie(yy revolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.dukqmdnyyp). zdn 1 0;*p b4;b5 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 in a w ovxqm2ib3s.5h5 z-dxhirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching it.s5bqv 35 x m2-diozxhs 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 240m+ c06o1a 9 bd(xu)aqjqtdot, rpm to 360 rpm in 6.5 s. How far will a point on the edge of ma1j6at0d+uq x ,9oc(b d t)qothe wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/m(ku tf-oz0nmz i62t-bin It turns 1500 revolutions before it comes to -b-zou(f n6tzt0k m2ia 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 m (/k4q6(4a 4 c bgwzeb*hzyediake 65 revolutions as the car reduces its speed uniformly from 95km/h to 456/(y*egc4zea(d 4h kibqz4b wkm/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces 9flc,cn fm)p5its speed uniformly from 95km/h to 45lcmn c9fp,f) 5km/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 wbh)wsxrh n 87-o.p,l zhen climbing a hill. The pedals rotax) 8wh-s .,zpo blh7nrte 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 for 9- za1jij np3orz(1ehc+b3muce of 55 N on the end of a door 74 cm wide. What is the magnitude of the torque if the force is jo(i cj3z1a+9 epnm ub1 zr3-hexerted
(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 f4k:9zlxo eolm-x 67 jthe axle of the wheel shown in Fig. 8–39. Assume that a friction torqx l:k6 m4x f9-o7eojlzue of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a massless rod whichi0 j zq6*4wa ji(/dere pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on thia/ew0ed 4ji *jzr6q( is system.

  The bolts on the cylinder j1(p97vofsxi head of an engine require tightening to a torque of 38 jfispo7 9x(v1$m \cdot N$ 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 o9io9ug m oe*can07cu7f inertia of a 10.8-kg sphere of radius 0.648 m when the axis of rota*em99no cciugo77 u0ation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in dia7)dyt nmw nwk8n7 .40vzqzw )bmeter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ignored (why?)wk 7q7 d)bw8z0tnz).wyvm n n4.    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in a horizontudw1al53ny.r0r 4(0pbmj o msal cird(urr lymb4mo1s5wan. pj030 cle of radius 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 pojf7aa4)8sq* .r d +u*k2w olils vz7tutter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands ankz2s jdtw74+8*v oal sa q l*ifu.7r)ud 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 object6odrwu0g4m t 9s shown in Fig. 8–43 ab90uw d6 ogtr4mout
(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 ofd+ ene *o6rm5lb zs,u; two oxygen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, unifor uq54df - 01vyymng)3 hudft1nm cylindrical satellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satelliyd guq1 0n uvn)t4mfy1d3 -5fhte is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylin-0h:gw o) iw+poa3mq dder with a radius of 8.50 cm and a mass of 0.580 kg. Calculatw:a h-d q)i0o+pm ogw3e
(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 ba(4 bn :w+whstii8; mvwbm-c: wt, accelerating 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 tangenti0w so;blw km()ally on a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-rl w;b m(k)0swoound 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 frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is;rsuyv 4w, /wp shut off and is eventually brought uniformly to rest by a frictiouyrvw wps /;4,nal 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 accep b w+e*uig0+tlerates 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*k-)b. n4 wcjl ch-pkpl6gd*y, which rotates about the elbow joint under the action of the triceps muscl. )k 6*jg*-bkpl w-ndcch yp4le, 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 canw9krh wu ngd781 4u6tk be considered a long thin rod, as shown in Fig. 8–46r gwnuku8wk61 t4h 9d7.
(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 mag() e(tx)vz4u c0mxzusses, $m_1$ 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 huwf 093 r;orolammer from rest within four full turns (revolutions) and releases it at a s;3r0oo l w9furpeed 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 me(f:;h (cc k0-kuslvi oment of inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque of 280 z2iv dad.j e)/$m \cdot N$ 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 ca: zkrpc.2, ui q/(iva;dci,k m rolls without slipping down a lane at 3.3d2k:czr ku/i(p v ,.;aiiq,c a $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the sum of t3zrti w-;hq;bwwb3t;h-i;z qr 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 hasw2mgttg sf)/31u 7hd c a mass of 1640 kg and a radius of 7.50 m. How much net work is required to accelerate it frot2 hg7 )3/g1udtfsmcwm rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and rolly9f.d. soqouf27ockb +z5f y2s without slipping dow. s72zk.oyb qoyof2ud5f+9fc n 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 fallpi2t7/yy i k4cxmx15dgr 5 ao6 and its lower end does not slip. What will be the speed of the up6 5ia5gy/ix1cx 472oym tdrk pper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular izdf 6o. pnwp)59q ke2b fa;bv/u k(/hmomentum of a 0.210-kg ball rotating on the end of a thin string in a5 ( n /kohk.bp96q)iaweubpdfzf;2 v / 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-kg uniform cylindrical griqbf4nh37 ci1 86brr fdnding wheel of radius 18 cm when rotating at 15 nb h143rdr7fq8 bif6c00 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 hi.-c /fs ceaxhdrv :qmu/n.x30s side, on a platform that is rotating at a rate of /d r x0m./c:-qsvch xu.3nfae1.3rev/s If he raises 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 Fig. 8–29) can reduce her p0/ 2;ywk,d,g7 ryg.dunr pwsmoment of inertia by a factordr2,n,y0w/;gs y7 k.wudrg pp of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her y;-pcm*8nbe ospin rotation rate from an initial rate of 1.0 rev evemnc-yp* ;8ebo ry 2.0 s to a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axis through its center at a 3 n hzh6tg/bgff -mo0,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 center of the rotating wheel. What is the frequency of the wheel after the clay sf 6nhh0 /o-3b ft,zgmgticks to it?    $rev/s$

  (a) What is the angular mse tgk4suf v43k;r73v omentum 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 momentc h41 uklm8cb6um of the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of iner,sb2gy ;tj5vatia I is dropped onto an identical t; jvsyab,52g disk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at/ n(a hheoxvuz4oi3; ( 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 pla(bnk -u )1rcp3afqgx2tform of radius 3.0 m and moment of inert( f)xr -k2agqbp1 3cnuia 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 free,snh7+n1i cpd ly with an angular velocity of 0. 7hc+p1,nnsdi 8 $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a white dwarf, lp6n19z1 6v edtl14mdjvitr8 y osing about half its mass in d de8z1yt v9tm6ip njvrl1 614the 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 involv*z2k/kr n 6h 8 tld+j;w-rpvgsn,ra7pe winds 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 y*a-o jbg.3gd g8.jcn$ 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 lqmz:.r cdm( .platform, initially at rest, that can rotate freely without friction. The moment of inertia of lq. d z.mc(:rmthe 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 a 6.5-m dqmu a*w,-f2p2+ vg iieiameter merry-go-round turntable that is mounted on frictionless bearings and has a momevwq+ag2m2f i p,- u*ient 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 ground with o,ps ,o/0qf( ;kwnp anc1wwz0the end of the rope lying on the topzc0o1( , p/nk,wf;wwqn p0soa edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Eapwex)nl +bbk/(;f v 6ozg;8f frth 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 particle orbiting the Eb;+; 6 v )gpl(xfoek/8bzfwfnarth.)    $\times10^{ -6}$

  A cyclist accelerates from fgz-g 4-uxdw: rest at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cyli0ce+5 x :mgxifr 5gfk,. i6fpnnder of radius 0.20 m acquires a rotational rate of from rpei g: xfn55i0 xf6crk+,.fgm est 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 lx99ffcftxr va z 265.c./:yf ccf6fysolid cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservatif6r.xf95: l fcfca.z/ y69yxfftc 2v con 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 the angular speejolp+m c0-)h2azew bcr zx rqzh(-286d 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 grnu/;wibd 3o/ ch4ke*t eat, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the procecbou/wk 3/4h de *it;nss, 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 x w2u2 a*ba;rq)hecm 0p)noy9to use energy stored in a a)wa* rc nqm9)e;op22bu x hy0heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustratez oh1 h.nv9n/7bjm8b fs 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 horizont1/daywo; :nk+c tijv5al 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 giu;y3s0 v3rdsanj ax29*tw a8 .vw:gignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment o; jusra wa9ga0t*.8svx2di 3yw :v3gnf release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on the floor, and ;3+nl5hz6:f zbxkge bwblm )8we want to exert a horizontal force F at its axle so that it will climb a step agaie85mk gbn 6; 3:+bz lw)blhxzfnst 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 hi.rvr;p4r l:*wu rr :-(ennqroad is making a turn with a radius The forces acting on theq.e*u n(ihr-:rrl:;rvw r4 np 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 0.5pw.xglrqy n4pt5b*6t,fd /gudqr cs6v727 / z0-kg rock into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, 2p7qb n5gwr 6g6us*p/x ydl4tz7vq, rcft /d .and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylindgmja624ph re ll3 6v0f/wpu(ae+i a7qer and her arms as thin rods, making +pafie( a6mj/lhv7ew60u gar32 4plq reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists xfwx7mjqf7vls;x,95 of two cylindrical plates, of mass5jfxmx 7w9 qf7vxl;,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 looped rou7bb0 6gjn hu5/db/gjqgh 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 pointqd/hg 5gu/ bj b6n0jb7 of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assume2p zuy2l:,pph $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its 3 pg/ts8ouro/; +j ntte (kh*rspeed uniformly from 90jk38*rg t/;h(sru/o+ t tpe onkm/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