A bicycle odometer (which measures distance traveled) is attacheinv (7ooiz2 5 gw)/d1j gyr:aom (1wdrd near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24/ yjwoigv7w1 ((mrodz1 d:n g5i 2aro)-inch wheels?

Suppose a disk rotates at constant angular ve : 5d ,)im 057vpo :svdkbmyuzoljmh*)locity. Does a point on the rim have radial and/or tangential acceleration? If the dis)l5dz0u vd ::,75sovbk)m p ym *imjohk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be describv24 bwuv2fbjvqlt; 27ed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a lv)-l7x zea qy5arger 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 sithxtk /wm43ap0 -up with your hands behind your head than when your arms are stretched out in front of you? A diagram may help you to answer xkwm 4a0ph3t/this.

A 21-speed bicycle has seven6(v pvh,(spn 2 fmee;1f)wret sprockets at the rear wheel and three at the pedal cranks. In which gear is it harder to pe2t,) s(r(pvn1fepeef6hm ;v wdal, 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 front sprocket? Why?

Mammals that depend otg;kfer3 niov3od85v1o f n(7 2kn;s un being able to run fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dyr; n32fiesknu3 v ;5vnofo do7 1t8gk(namics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35n btmryac***iu33t3p7+r w ni ) carry a long, narrow beam?

If the net force on a system is zero, is the ne(wi zeh+ane* :t torque also zero? If the net torque on a system is zero, e(nh:aez+ *iwis the net force zero?

Two inclines have the same height but make different xo1;w/ vya6y+flpb(t angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom bva ;6+tl/yy1 wof (pxbe greater? Explain.

Two solid spheres simultaneously star rs*l/mg d-lz,t rolling (from 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 the brd* ls g/lz-m,ottom?

A sphere and a cylinder have the same radius and the same mass. They stb-el:6 ;sd zbn4llix4 art 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 has the greater rln4 :eil6 d;l bzx4sb-otational KE?

We claim that momentum and angular momentum are consopcyr 3u1tce z; 2)a1cxq; d/ycaw /g1erved. Yet most moving or rotating objects eventually slow down and1exyg c2d)p;a1q at /r1c3cou/;yzw c stop. Explain.

If there were a great migration of people toward the Eao)b zk-dx 49pgync opwlj,55-rth’s equator, how would k -ojbp)5w4z5lnyx gc-dp, 9 othis affect the length of the day?

Can the diver of Fig. 8–29 do a somersault withoutdfai5y guq+to/6f,. n having any initial rotation when she leaves the boar ua,y./5+fq nd 6goitfd?

The moment of inertia of a rotating solid disk about an axis through its845h.d3e ft+uwb eiw nndq/.w center of masit3u8w.qf5neen b+w dh.4/wd s 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 in each oubv s:-w8uyq2 atstretched hand. Is:ba vq yu82-wf you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mar dej0mz3myao*y p 0mi2.l:p)2g um+ass. However, one is hollow and the other is )jro g 3:2imy+p2 mlmu*yz aa0d pm.e0solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horx5x/zj)9vlqro14q5q(fjpixu* d ug , u/s4bmizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this poi1l r9d x b/j u5pj *4guq)xxq4v(ou z5,s/qifmnt at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the jk7pmx4d pd63edge of a large freely rotating turntable. What happens ipkj4pm 63x dd7f you walk toward the center?

A shortstop may leap into the air to catch a ball and throw 7 ow6i.rh3;isg)ugoof r6d+c 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 directi i;36rro sgiohd6cwu+g7f.o )on (Fig. 8–36). Explain.

On the basis of the law ofyhb2e09f: kx r0n vsbz: )w7xr conservation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or: 7v) w s0e9hnrfr02b z:yxbxk more ways the second propeller can operate to keep the helicopter stable.

  Express the following an(tk m)u a ,xxbkz rui/u(2y/f(gles 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 cop9q6 c.fr fc,lincidence. Calculate, using the information inside the Front Cof c. ,9c6qplfrver, 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 Moon, 380,000 km from Earth. The beam diviq ) ,qnd4e9fxerges at an anglqf4id9x)e, nqe $\theta$ (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 6508q3s tafq8,upo ft z+80 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades st+qp fz oaf38,s8utq8low down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. Ifc i6lkz+ptf gevwd 2gor+77( 4 the ball makes 15.0 rwr6lt ied +7 v(+ 42okfczggp7evolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diametzb v37.ujsn-m er travels 8.0 km. How many revolutions do the-ms.7v j3bu nz wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate its a a- ylgf (7( 1v0qd7lu2zmsgbnngulz7s-bd 10mgvl(a nlq72gfyu (ar velocity in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolution )a( u+-yv1zr4 llnpuoin 4.0 s (Fig. 8–38). (a) What is the linear su) purz 1+4nalol- yv(peed 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 (l 2oqnao6xs v nc;9fk(nt31 0mw rwm;velocity 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 speed of a pow4xe+7 vb6lte. :qqrhji 57cbint
(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 rrrrq:up f ,)hc8hsa- -otate if a particle 7.0 cm from the axis of rotation is toarh) c-srf- r,8huqp : experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center /b)(uq+g z ves4snoq7from 130 rpm to 280 rpm in 4.vqng q+( 7)uzboes4 /s0 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 xutpw ctvm0eevyl mz;f,iu3k 5z q)/4y :(+w) $R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$

  In traveling to the Moon, astronauts aboard the Apollo spacecraft put g-cjp u sptg,oq)2tuz: 1zn)w( xx0 m;themselves into a slow rotation to distribute the Sun’s ene:ptw-jz)(x 2,qtozc xu1gpnm)0ug; srgy 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 with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm in 270kevrry*: qp d:trh7 20 s. Through how many revolutions didqdkrtp*0:7:r7ev rhy it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Calculatay m/:a w8y+ us(-hynhe
(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 whirling “hq 04,k lnsb,5 tw: fx*8kqzozzuman centrifuge,” which takes zzx5t8no,l4k,q k 0bqzf s*w: 1.0 min to turn through 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uni1b o je,k5 9ukt58cyr;qjm i5aformly from 240 rpm to 360 rpm in 6.5 s. How far will a poinie8kb,yj1;5 k jcq 5u9toa5mrt on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850revtma;/ fsv-d.msomkyo5 7- 4df/min It turns 1500 revolutions before it comes tom/ykd mf-7ta5;o4- vs.sodmf a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as t-afvlao4 e 7g7he car reduces its speed uniformly from 95km/h to 45km/h 7o4 lave-7gafThe 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 its speed uniformly f(y7u0 b -ydaofrom 95km/h to 45km/do( yb 07y-aufh The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on each pedal when climbing v2ne;( vyz 8mq7 )chyya hill. Th (; vcn7v2q8myyey)hze 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 f;1k rym:h/+.x m+t zguk*v eya door 74 cm wide. What is the magnitu/ek1.++kzryht ;m *fvux:gy mde 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.cn ydsk*k ;o*npp0*f+ 8–39. Assume thk0n p*;*sk+ dy *npcfoat 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 attayp7cy9.6ja;y fvidt 1 ched to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the ho6vp7tc1 fi yja9.dyy ;rizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require ijuxo,x 9d, +k;bljt5 tightening to a torque of 38o+jj5,9li kt;x, xub d $m \cdot N$ 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 m when the a w 0of:mwkf6r.xis of w0ofmk.:w f6 rrotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of5hy1yom7f9 t(e6 epa4d6 raoo a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the o9efoy 5r6t 4(17myaho6 pe adhub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in a horibvgb x.m) dd 00bn,i-28bbicazontal cirbd0b-dgvb, xc0ai28m n.i bb) 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 potter’s wheel rotating at constant angular8xx p9 gxlkks1vm 02m0 speed (Fig. 8–42). The frictsm9x2108 xkmlvgpkx0ion 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 theozzuylt- 4yv0 q)u7b)kgh:(u array of point objects shown in Fig. 8–43 abt)yz h:g 4o )(k7z-l b0yuuvuqout
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxygen atoms whose total mass i**. jq( cm gcn8ca 8+dnkrosx;3z+jmsrg 9 ah)s $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning 4a. ,bmzapko kf)-q/ dat the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass ofqkd,fp/a k-)z ob.am4 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 gar j; msqk*38d:renz 7rs; k5mass of 0.580 k m*d ;jq: kazr n;s8gr3s7k5erg. Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerating it from rest to 3zo0ajm1e5+m2s w5s bp $rev/s$ 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 smal tmvonni*8e z-+.x-:e s +fugll hand-driven merry-go-round and is able to accelerate it from rest to is v:*me uglfxtz.en8+- n +-oa frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is s1 72h(dfuqrt y2q3dnehut off and is eventually brought uniformly to rest by a frictional torque of qy d(tr72n13q 2hefud 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–xe9m c)fn- -cz45 accelerates 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 8 +am,yyziw-uaction of the forearm, which rotates about the elbow joint under the action of the tricwy m8za, +u-iyeps 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 5cr9 x,q1r4cq6bog tx 8nuf-nlong thin rod, as shown in Fig. 8–4 ng1t r9qcnx6of-c xur84,q5b 6.
(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.    $kg \cdot m^2$
(b) How much torque must the motor apply to bring the blades up to a speed of 5 $rev/s$ in 8.0 s?    $m \cdot N$

An Atwood’s machine consist 39xv+ mke2ez/uf y+ea2viyr 7s 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 full turns (revxv s iaito4ju6 z(841bolutions) andj1vu8ai4(xz6 otbsi 4 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 inertia of q2u t l+lmap4 mw12mka:4:esd$3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque ovd1x/i/w z9psf 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 rlmby0*0 kalg 7olls without slipping down a lane at 00a* ml7lkygb 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with-- onv3qzo/d m7 h:zob: sczxr8;hd,c respect to the Sun as the sum of tm 8d qv-c,b; 7n zh3z :cr-x/sohzoo:dwo terms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.50 m. How much ne-eub, z 4sz yohf4)6ltt work is required to accelerate it from rest to a rotation rate of 1.00 revolut etb4zy )4hflu6z-s,oion per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg s5(fh(3o5yj tgkh .qvd 2b pa1starts from rest and rolls without slipping down a 303 s2 5j(gophb qy.dh1(k5 vaft.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 balab u2;dn;z 7f uf64goelnced 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: Use conservatio;de2u lugnboz6f4; f7n of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the en ;,n4 ef/awty )z+ 0xp4ko;ygeb k,kwhd of a thin string in a circle of radius 14pk +w/)x o; e;nyt 0gyk4eahw,b,fzk.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2..z45arvm76 o i7qs 6trcqw:e w8-kg uniform cylindrical grinding wheel of radiuv7tcqer: aq ow5rsw 6i.4mz 76s 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 hiv v /f9 ky,)ek(bpgoj,s side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decreases to ,gyjvo) (fvb kpk9/e,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 redu1f; j seha 3kptnvdl.k: 2,;upce her moment of inertia by a factor of about 3.5 when changing from the straight position to, ndtl1.; k: fpj;uvek ah2s3p 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 rate from an initialx xa it,:+roz4tpz1v3 rate of 1.0 rev every 2.0 s to a 4 xxttp1z,ai:3oz+rv 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 ve;c1p6 4 ;)trnxbuyzxcrtical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.4;) 61y; zp4xccnu xtrb0 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 skater spinning a j*z2ofxt9 aqw6 0bi5aqnv24vt 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 j+azwey tn +;y7wf:j4of 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 inertia I is droppe :n) uplnaw;3 )lfs:ebd onto an identical disk rotating :3u;)aw)nbel npslf: at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns tkxwe0te a/5) -4yv syat 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 chwhk.5yyr.: s6) vhxyenter of a rotating merry-go-round platform of radwh x.yy6.h ky5r)vs:h ius 3.0 m and moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is roel-gszg6*s*4 m c1k wotating freely with an angular velocity of 0s ekmz4 g* 6ogc-1wsl*.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 cd3 q,tpba 15cfollapses into a white dwarf, losing about half its mass in t,bd q53fap1tche process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve wind8icv6;;oyjwau.n7ax s 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 x;/fsp ikjj6 wz5u7a0$ 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 withou m8z atb*;zr. eus0m(at friction. The moment of inertia of the person plus the platform is 8.a rmtu az0(b*ez;ms $I_P$ 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 diameter merrv*m,sj8f u ,jty-go-round turntable that is mojj,u vt f,*8msunted on frictionless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the grounw 28zd,jazrg86 g9zlwd 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 unwinds from the spool? How far does the spool’s center of mass mov9w2 z,z8w gdzar86g lje?

  The Moon orbits the Earao4ay9) 7: nfzggyg(sth 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 Earth.nfgs7a ya4z:g ( )yo9g)    $\times10^{ -6}$

  A cyclist accelerate;au2zwx.6 kh(78n p xceufe3 js from 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 nwjc.v)81ay4szm hbq xe 0.jk0: l9oiof a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant he.:jqkyosi0 nxjm wz9v41) c0al8b .angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylicc-n - mhlew::ndrical 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 s -cnc-:w lhme:peed 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 -qb +sky(akxzfax a/xo ;(i;3speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 times as great, wv rmtac v,843eere 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 process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that e t 8cvrav4,m3the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a lcm;k/zf(py 8 eg e3m1wow-pollution automobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total ma p;3z m8w1 gf/(eekcymss 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./1i ye nd5klf 7ip-qh 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 surface at s3h8wpiw;y/f/a d:np z peed 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 fre rkljrky-+4g9yz*1zmpljt7 +b+um9lely (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. [Hiygk-m* k 4y+z9r9blu+z jltj7l +pr1mnt: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on the)l,e8 ca+jzgsumjx6 y mx7.;x floor, and we want to exert a horizontal force F at its axle so that it will clijl x x8zy +.)7g, ce6jmmua;xsmb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is making a turn w5kj.er s7iex+ ith a radius The forces acting on the cyclist and cycle arks.j+ 5 7iexree 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-kg rock into a sling of length 1.5 mgvk*o me07as: 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, and where does the torque 7 0*:amvo skegcome from?    $m \cdot N$

  Model a figure skater’s body as avek j61g6t. 1rjjsmx+95h0 rp- jucvg solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning sk grmkte1 x 5-6juvjrvjs 91gj6phc+0. ater with outstretched arms, and with arms held tightly against her body.   

  You are designing a i9 lm rbpcu0czw o; 9crnnnx:+-;+li )0tdki 8clutch assembly which consists of two cylindrical plates, of rcnz+x w; tnpdkcou00inl-i m9 lr9 b;+8c)i: mass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 radiu4, mc c0u1v6uft8necfs 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 reachc 0ve1fc 64 fmu,tcn8u the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but dmhs+5a jatt /9m*0d zejyn18lo not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed uniformlle qh2x2u 34agy from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular a x24 ehqgl32aucceleration 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