A bicycle odometer (which meapuc2.vx8 3bnwdnt,i, e9 5b ggsures distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use ndngcb3 , ,28w e. b9g5utxpviit on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on the rim hav justpmic4qf0l2m0)3- e h;ox*t ima 8e radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleratia muflhm4 0;3oji-cmx 8*e)ts qpti 20on? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the angular vtx9 /t5 sooh1acf+ *f/ai:xe uelocity $\omega$ Explain.

Can a small force ever exert a greater torque than7xc ao wrzw)uhe5f fk198g6*q 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 behdl.t ( fw1zutu) 9u;dvind your head than when your arms are stretched out in front of you? Az1(; ul vftu 9tdwu.d) diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rwe nnrgeb *f69l 822n (siz+-mtz)zujear 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 large frin z2e-6z+un8*2rm g)(wz9ej n ltfbs ont sprocket? Why?

Mammals that depend on being able to run fast have slender lower legc* 4+4l(kh sl2qngg9l d6( u-j sp+ra s-lazfms with flesh and muscl(+jas69 4 mfuglsl -r-4*n+ paldzkchsgl2( q e 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,915nv(qwf1m rik z6v z narrow beam?

If the net force on a system is zero, is the net torque also zero? If thy: au8s646ac 3a an7j6 aovlhqe net torque on a system is zero, is the neta q 47v:ach6 laoyn6j3 sa68au force zero?

Two inclines have the same height but make different angles wij*tswa 1r jfs5muu5dqbc56 lsob32/. th the horizontal. The same steel ball is rolled down each incline. On which incline will tj6rbbl5tda wc. 3u fs u*qj/s51s2 5mohe speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling ()3solu phl. p6from rest) down an incline. One sphere 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 tp)lsh.p 6ul o3he bottom?

A sphere and a cylinder have the same radius and the same mass.6zl+f6gfssjft/n a*2 They start from 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 at the bottom? Which h 6ljs/ fgzf*t+sf2n6aas the greater rotational KE?

We claim that momentum and angular momentum are conseraj:tu9c/ *5sbbavgo *ved. Yet most moving or rotating objects eventually slow down and stop. Explain.*j:5at9* vgbabuo/s c

If there were a great migration of people toward the Earth’s equator, hy g/j /cll,hz;zri,hsadf)6j7 8kq h7ow would this affect the length of the day,,7;h6)y d z/iajsq czfllh8 k /j7grh?

Can the diver of Fig. 8–29 do a somersault without having any initial rotation jvw,mwi9a2rh k+1h: jwhen she leaves the boa 29jmi,wr1 whva+:khjrd?

The moment of inertia of a rotatin5a 1kt-,:7idm rcpdfqg solid disk about an axis through its center of mkd:p fm1a-5d ri,7tc qass 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 hode 0+.7panw wrlding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay t wd7pr we.0+nahe same? Explain.

Two spheres look identa;;yhprqm a/ :ical and have the same mass. However, one is hollow and the other is solid. Describe an experiment to determine which imyhaqpar;/; :s which.

The angular velocity of a wheel rotating on a horizontal axle po(;r/9 siy6aa3iya 1r 3l bxpbeints west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increy px36;rba(i isby 3leaar91/asing or decreasing?

Suppose you are standing on the edge of a large freely rotating turntable. W1,fi mt q,k/s j+jijrtqh)e5-hat happens if you walk towaq fr)j+i th1-i /qs etjmk5j,,rd the center?

A shortstop may leap72 e v-bhmcii2* ,i6jsu 2knfp into the air to catch a ball and throw it quickly. As he thm -fk2isv2i7,hb c*i ue 2njp6rows 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. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discuoa:i+b 8x( +uovu7khzss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second prohxk(+ 8 uooab+vzi7 :upeller can operate to keep the helicopter stable.

  Express the following angx9+ ,fsfd6 z1( 1lcp.l mugv,io/k tfples in 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. Calculats nf do)+hy5bpdgd/3o +jp n2,e, using the informati b/pjsy5) +donf+nogd 3,dp 2hon inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moo juf qv72(em5cd mk/-kn, 380,000 km from Earth. The beam diverges at an/7mcu qmkk2e(v d- fj5 angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. When the molkc4xb* wvf s9ow, h;1tor is turned off during operation, the blades slow tk 9xws, 4bcvlw;f 1*hoo rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball ot5uii. nd uid7daw( v731jgi 7n a level floor 3.5 m to another child. If the ball makes 15.0 revolutidij5 ii(iwgnv7 tua d3d7u7.1 ons, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolutions do n4z4 . r6b;0:xji vnlewd eaa;the wheels dn4na.i0 :a4;zexwv ljb;e6 r make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 250ii4*z nmbq +1 w8 n063mm s:pxd)ofcxw0 rpm. Calculate its angular b:)m6 i84s q 0w pmz+1d*xwnnxmfi3ocvelocity 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 comple4* kc)*(xucy+r khg akte revolution in 4.0 s (Fig. 8–38). (a) What is the link)c*(+ 4yhk*gku cxarear 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 its orbit a0ung*. g :iad2 t,quvground the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed o3c:+b8knsl-gqvwj,+j d (6 c n qszjz;f 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 centrifmrx-poe3 7cmy ; ab-p-uge rotate if a particle 7.0 cm from the axis of rotation is to experience an accelerationc-xo a 7pe3-; ymr-pmb of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter whea0z;)f c l1j7x my8+hsmwbrx2j13(u2mps ewcel accelerates uniformly about its center from 130 rpm to 280 r0;me2l1c u(8)wwcpzx7m23 1 r bssx+m jjyfhapm in 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 radiurxgw: uj;kzd6./blv/ 3y4nlp(c omq-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 Apoawq9 (b(-w/ 1ocskfig llo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At t9qbf cs/1owk wiga( (-he 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 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 accelerate +xo *pjg;kquw*k9:9 mrx8ouj s uniformly from rest to 15,000 rpm in 220 s. Through how many revolutions did it turn in this ti9ouuj8qk *+* :px9 gwjorxmk;me?    $rev$

  An automobile engine slows dxuy -)r.f 6 29zfidkv;ct1-tm0/qv d/ftyel f own from 4500 rpm to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested fouvwt38 sid:q5; u(do rr the stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to tuuu8r( o3 5w :didqvst;rn through 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates knj.; nac3z*zu:h2zk uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel hz2nj h k z:*cz;.un3kaave traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 1500 revol .s 0:vz:qjocoutions before it comes to a stoozc0s: j:v.qop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed unss .t; 01ksldiiformly from 95km/h ttl10is . s;dsko 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

  The tires of a car make 65 revolutions as the care7frijs2gbmz v-5n)4+: bn jo reduces its speed uniformly from 95km/h to 45km/h The tires -m j4v)j7gi+b o efzn5:rb2snhave 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 putsk8d i,o4ngps 9 all her weight on each pedal when climbing a hillog dn4 sip,89k. The pedals rotate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door *gd y 7nhf ;g;, 4ev3:likeond74 cm wide. What is the magney;d;:7einglkfg4* n ,d 3hv oitude of the torque if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel shown in Fig. 8–39pr4jg/vc -a:h1 kwk)h. Assume thk:p h/41hgkcw-) jrvaat a friction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are adpz/7p3tom;d4. o,a h;nahb bttached 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. Calculate the magnitude and directip bdhadb;zh3/m on o.;a 7p4t,on of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening to a torque 2xw r wdcffivex0::/dksh +.4xev (2u of 38ee0iu2wv (r4kxfsd hx :dv2w/+f:.x c $m \cdot N$ 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 0.648kn2g1o)kem d3 m when the axis of rotation is thgmd12onek3 k)rough its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diam 5-fyee5m zl/yj (w;kreter. The rim andz w5rye/-mlefk(jy5 ; tire have a combined mass of 1.25 kg. The 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 rotated ingv.vv/ 80b- (zsehv o0i7 cjdv a horizontal circle of radius 1.2 m. Calcov.zj0 /7geh8vi- 0cvvb (dsvulate
(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 rotating at constant angular sprm ez; -vo;d eonz76 4zo-9nmfeed (Fig. 8–42). The m9o en -7-vmenz or;4dfz 6z;ofriction force between her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of point objects sabh5plak/ rggl5+iea1 o+mwn e492c wx2(7r qhown in Fig. 8–43 +bw k go2l15rr hx+2/w5i(lcmpqgaee7 94 a naabout
(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 oxyhh-5s4azy-pt+fulu 3y;rvics9n3 c +gen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satel om*as5mon mv2a xi1)7lite spinning at the correct rate, engin mo7mo* s)21xn5vi amaeers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm and a;ldmn 4mfu0 *d;ikgu+ mass of 0.580 kg. Calculaf*dmi 0gd;klnmuu4;+ te
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerating it pxfqo1 xvd0fk)jl2 7. 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 sma/0nx5yl/dvw ,z t)n spll 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, lptz /s5,n/wy xdn)0 vneglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off a/ 6;kyic gfo5dnd is eventually brought uniformly to/gc5yko fd 6i; 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 accelerates a rw md6/3m1 -e katsrg zsv4a303.6-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, ;jwh,yt, uurxfi(5,lm: dgyxxim4 ++which rotaty5hxl (:gixm,jrwd+iut;fux ,y m4 +,es about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thin rod, as (w-zp/wo1,mge3 wgkyshown in Fig. 8–46o3wwkzg/m,p (yg w1-e .
(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 c2n+gavp/9 l6iht6fl sonsists 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 hammer from rest within four fu2buam:5;jn )lv ko- yddb -f3tll turns (revolutions) and releasejdmokt2 bu:v3a-b n) dy-l5;fs 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 ine f)/dh9/ 5hhkhq(kayo08i hyuw/dh p-rtia 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 developg htjd 1:we0)bs 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 rollnae o))fl.ycj /kv ,l0s without slipping down a lane ay,)o.cj ea0)vf/ llnk t 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the s:7u 5 h*fbpfrsk 9n kiud07ix*um of two te 7du7r iu*xk*p fbhiksf0:9 n5rms,
(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 m9+ injk 54 eikzrvj vx*/3agcjqu5z 90ass of 1640 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotatiojrj va5 * 4cui5k/vj9qk0gn+ 9z 3ixzen 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 an bmo4kx,y0h9g d rolls without slipping 0 ghkm,b4oyx9 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 verticallyl0ly2o 5czmlwd 0a 2l5 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: Use conservation of d5lom ywll c zl0a5202energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the end o ,gou,x7g70vmmvgru 2f a thin string in a circle of radius 1.10 m at an angular speed0g7,,2omgvrgumuv 7 x of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grinding whefm3ajmf .qlx)vv) m)3el of radius 18 )vm )fvlxm.ja 33f)q mcm 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 n3ek.suz 12zv platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, sk.uz1 e2zn3vFig. 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) c bue5n3vj.f) db ,-1 mkwonaw5an reduce her moment of inertia by u1vo3, 5abkwbjw- en5n d)m.fa factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation r7f i/p le l(10 seisem7lq-9wi60nquw ate from an initial rate of 1.0 rev every 2.0 s to a final rate fnuilm eq9 le7liie0wsp0/(7 6s w-q1of 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 cf:mb:*/ ept qaenter at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m.e::p a/tm* bfq 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 m qsw q92ah92kfigure 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 m .a2 kdx,2xeenomentum 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:kzm idn17 8crr:g0v xtia I is dropped onto an identical disk rotating at angular speerk 0zgr:id8 vxmcn17:d $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns dx3si:6p s lm3om:zv9 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 ldmd 0 ylx30x5merry-go-round platform oxl0d 3m0dyx 5lf 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 meryzwlpy)q,ii+:m *o myp.r x( yys/f88ry-go-round is rotating freely with an angular velocity of 08(i,ymrqf mo *piy:x y)swy y./p zl8+.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 whwjfozf 6 z8(q:ite dwarf, losing about half its mass in the process, and winding up wiz o(w zjqf6:f8th a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in tf.2 zg6f;c wx; slxl;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 u7hogszl -52r7lmz- l$ 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, thkrlvt+)9i wip8b41i uat can rotate freely without friction. The moment of ineriur+l4kv8 pti)9b wi1tia 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 (-/k -jlbr jnp.brgs( stands at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on fric-l. b(j pns(-jk rrg/btionless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the gg8l( q3gi f:beround with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwind:fei (3g8gqlb s from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side alwauquuz q7.y9p ;/n q+zcys 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, tr/quqzz7;u pu+cn9 q y.eat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from ji o9tlvx8*q z d::/parest 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 ing+o lk;6 7uhaws vd 3qh3a+4wk the shape of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque deliverek3o havh+ +a3glkdu;w4 q w67sd by the motor.    $m \cdot N$

  (a) A yo-yo is made of two soli kzu7l xa8dy8/d 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 conservation of energy to calculate the linear speed of the yo-yo when it re/8auk zy87dx laches 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 a hrky2 /nnyh-1ngular 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 Skxp;;q,u (-xt gagoy:un, but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutronyux-( ao;q; ,kt ggp:x 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 u fcq-a5b )koc;se energy stored in a heavy rotating flywheel. Suppo) cfo-5 ac;qkbse such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrates ahy- 3f kb1be.vq g *wz+yvt(;wn $H_2O$ 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 o8td s*grodzauu) )rzr c k*(32n a horizontal 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 f/( eo0g;kgmal bppm ,,reely (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 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: Seelppe0kmg m, ( ;g/,boa Fig. 8–21g.]

A wheel of mass M has radius R. It 5q8e:l(qk bp:b4yap:tfdm 0 p is standing vertically on the floor, and we want to exer(4a0f :q ydtpbepm :pbk q5l8:t a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat sm.88 u+mtf ogd up+ /dur c+9qevas59road is making a turn with a radius The forces acting on the cyclist and cycle are the nor+tacs5r/+9u m q sdg8 uep8om9u d.+vfmal 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-k xg7gy71a,j ebg 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 achixba7g ,7e g1jyeve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinzg)z -to evur7,3uu)kder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and w,3uz to7k) e)ru gvu-zith arms held tightly against her body.   

  You are designing a clutch assembly wpbsic/6,kd bx1: u*a khich consists of two cylindrical plates, of 1 a6x/,pbidks:c *bukmass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 rough track of Figwu9v8uk)iz k2*kok7dj:o7 j m. 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 loo2k kokoudv9jw :*k)8 7z7 imjup without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do bkxr;) bim7c*sjek)7 not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduce2twpr8,o: h y)ks.yx rs its speed uniformly from 90km/h to 6to) 8,2r yyrhkswpx:.0km/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