A bicycle odometer (which measures distance traveled) is attached near tghx60jz f- sd1he wheel hub and is designed for 27-inch wheels. What happens if youd6z-gx s10fhj use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a)w7x c0:o iekb point on the rim have radial and/or tangential acceleration? If the d0:cbi okxe )7wisk’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 bodyq6j;f5vp l 2z1jud/d.f8fau5jl sse ( be described by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque tn 7,l1mo t(;u;mj ncxphan 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 difficultc9.f9 frjllqnhz4 6erj*b nrq6e;.h 9 to do a sit-up with your hands behind your head than when your arms are stretched out in front of youhn;b9 zrnc lrj 9 f..6hqeq*469je frl? A diagram may help you to answer this.

A 21-speed bicycle has seven sp9kv i3m :ho1fff .* vcph6nm)yrockets 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 large frontmmi*n.v:pky1 9o)hv6 3fc ff h sprocket? Why?

Mammals that depend c2,*4*fo9 w acqruyzkon 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 rqycc *4,z29o*wau fkrotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) caa9x4 p (owl k2)e2mfwyrry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If the drcdi; )u xx+k;b* 1janet torque on a system is zero, is the nedj;*xd)x;ua+1crkb it force zero?

Two inclines have the same height but mak+5s9l;q 7:bai qtl ppfe different angles with the horizontal. The same steel ball is rolled down each inclif9ppl:5i; s 7tql +qbane. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rol ruxs7c(0)kmp ling (from rest) down an incline. One sphere has twice the radius and twice the mass of the othe(ur7s 0kxc )mpr. 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:pzlz9* alwa)5b0f 4.nzpux b ,k,b fe 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? Wbl4,l9 0 ba5zkzfpxf*wu.)z:,aepn b hich has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet m6n.af0;os:b xt fdy e:ost moving or rotating objects eventually slow down and stop xsty0do:ffa:e6.n b;. Explain.

If there were a great migration of people toward the Earthi 8k rhca;/+jo’s equator, how would this affect the lengt r +co8;j/aihkh of the day?

Can the diver of Fig. 8–29 do a somersault without having any initial roos (nu: z3 6ml2ho trdi *0nuh+0eom5atation wh 20 n oedh3mnhum(su*o+6i: 0ltz5aroen she leaves the board?

The moment of inertia of a :yn5q7c lh9ldrotating solid disk about an axis through its center of mass i 5l:9 h7ynldqcs $\frac{1}{2}WR^2$ (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 e4u / zhtkz5:p yziv17dach outstretched hand. If you suddenly4:zp yvzk 157ud/htzi drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is pwd38or72cvl jd9v2; a,b k phhollow and the other is solid. Describe an experim,obh 2cdr; awkvlj82p pvd973 ent to determine which is which.

The angular velocity of a wheel rotating on a horizontalszy ajm 3nu-lt /k6-1:3uw0 vjv xrt2t 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 point at the top of m ts -23 av :06j3ulu rk1x/wnytztv-jthe wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating turntable. Wh2i p5u; t rrc/w r;r8 ob2qdhb(k1ec9lat happens if you walk toward the center2i;8e brqc(u/rkr5hbr 9 2o plwc;t 1d?

A shortstop may leap into the air to catch a ball and throw it 4wof2 dvu 7jh+lv w7.vquickly. 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 (+74h2vvf j uwlw o.vd7Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discuss kilp dn;wlx 69(ibo)-why a helicopter must have more than one rotor (or propeller). Discusn6;9l()xwpd i-bk olis one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles 2m3lzihu1/c zin 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 Earth0a+i3dgzsrwv:i0 n-l 3(n u zd because of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in r(-3sv0duw:diazn3gl+0 iz nr adians) 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 z8qeuaiu6s ;eeh c 6(2wq 6k.gbeam diverges at an ane6q8uuka(egc. ;s6qhw 6zei 2gle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender+i7u(oj-und1fdx g 3o rotate at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest o+fou-x13njd 7i gdu (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 ball mrvc r m*9r3 el0t4u.rvakes 15.0 revolutions, what is its diameter?re.3luvtcr r4* 0r9vm    m

  A bicycle with tires 2* g)v (e4vbc0y)j;q;vm jw afaautw668 cm in diameter travels 8.0 km. How many revolutions do the wheels make? c)q;y( 0wj vw4tavg*mjfv u) 62;ebaa   $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpmy(2z/35 zumy;h ,0wwa:o v7aih qe digg,p: co. Calculate its angular velocc;/v,ug5:pd z g( yhh2,amoeq oziy:3iwa07 wity 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 revolutionu5j 6tmtk5qoc/ /+ tx6pi cz0d in 4.0 s (Fig. 8–38). (a) What is thqumz 6 6c t5ockjtx/5p +0dit/e 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 its orbit around the Sun3fes+ u sc46gkhg1z wt/ a7-xn    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed7vvlsh*eds xv*/:bx b*n/ fp5 of a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge roto ffcf9f(o4j.n b6 /dfate if a particle 7.0 cm from the axis of rotation is to experience an accelerationdbo(f.4ff9 cf/of jn6 of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpm t(8 -csk jrw/ctmb4/dr o 280 rpm in 4.0 s. D- k4s(m8wbrc dt/ cr/jetermine
(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 radiusju;k8ty(i l8klqpsxmq 2n +:+ $R_1$ 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 Moose sp3q ik+3q/h/oj-bn, astronauts aboard the Apollo spacecraft put themselves into a slow rotation to distribup eqq- io j/hb3s/3s+kte 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 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 toyoxspaiwk irb8fnv;2/) 0+b. 15,000 rpm in 220 s. Through how many revolutions did it tubn; 8/pfia+rsv0x2k.y i)wbo rn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Calculai0wt2 h *.ldsfte
(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 whirlinf73ya9h, rg dtg “human centrifuge,” which takes ,h fy9a3dtr7g 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 uniformly from 240 rpm btg3. fh80ayi4pi 6ghto 360 rpm in 6.5 s. How far will a ptihf 6bgaih3 y480.g point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is*x; tz ufwr9yv x1-h9s running at 850rev/min It turns 1500 revolutions before9x1hy;uw9*zxfv r s t- it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car reduces itslzy.i9 p4t-na speed uniformly from 95km/h to 45km/h The tires have a diametet.9yl a4nz pi-r 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 redmj*wj9u bnqyu e2e+c uyc-*;8uces its speed uniformly from 95km/h to 45km/h The tires have e jn*8;2+yc*byc9uu mq ej-w ua 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 clr2+;:sb3w tb/zf h zani((u5k(f bni simbing a hill. The pedals rotate in a circle of radius 17 cm.;fb2f(a(kns: in3b5hu(/zs+ bzwi tr
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 5 l arsx9v,ivymnytt;g82*. 5ceij d225 N on the end of a door 74 cm wide. What is the magnitude of the torque if the force is exerted5 xdc2v8m9y2;. r ts2, nitaiglv*je y
(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 thev7ak xoofhm7pk20 +v8 axle of the wheel shown in Fig. 8–39. Assume that a friction torqu 7 kfv70 voax8khmpo2+e of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attachew .u3 aosc*dtfd lj1*:d 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 th:1oj. dclw*f3 *autdse magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engiq-f5tnu 2hl09if f)wene require tightening to a torque of 38 l 52)f-e fq0finuwth9 $m \cdot N$ 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-kgmb h4b: w-7)we8yz4 wxcxea3g/ hpgg7 sphere of radius 0.648 m when the awy h/xbm7-ge:)gwa8bzwg hx7 44epc3xis of rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycl9x sndhil/;1gr8z mx* oa.(xne wheel 66.7 cm in diameter. The rim and tire nm 9a( s8.go/*nxh zdi1r;xlx 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 .to,zdb(ubtm (yla ; .a thin, light rod is rotated in a horizontal cir.(loyb(b.t, mtda z;ucle 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 axmpy4 zj5in;x,l (oa0t constant angular speed (Fig. 8–42). The friction force between her han; 50lax( mo,yi4 pjnxzds 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 ofr im 7uw3jpd46vnip )1 the array of point objects shown in Fig. 8–43 aboutvwid6nr1 374puijmp)
(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 consisrg1k xb jut))9u75vitts of 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, uniform cylindrical satellite spinning at the correct rate, engi .p/s3h ptlqdge*k fuvrg9 28-neers fire four tangential rockets as shown in Fig.pskfe u v.qhdg2*lg9/8 r-pt3 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 unxnw1.k ;zavz j99ep j6iform cylinder with a radius of 8.50 cm and a mass of 0.580 kg. Calculatexwz.k61z ejn 99 ;apjv
(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 isyov c8fzh,, nu5iof or()5.wt from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-driven memk;,0gz1s hrco menvpcy ,,3p3 9nwd 2rry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torqdsyv2k,g , 3 mzc9wh;3m1,0nppnro ecue. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 .5-dr,yivhzai xx xs7(-e1kt rpm is shut off and is eventually brought uniformly to rest by a frictional torque of(z . a7s-1xxivy k5xht-i red, 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 acceu (;d)qa ld9*io pmxp-lerates 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 for8b(r(,fosmk eearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated unifos,(8f omerk b(rmly 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 c)8v6fdf *laoz onsidered a long thin rod, as shown in Fig. 8–46.d6a8)v *offzl
(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 masspwv0v i11t-sy es, $m_1$ 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 accelerates1x/(gxyfla 59 4e5ga g6dsmc vw 5cx;y the hammer from rest within four full turns (revolutions) an51/sa c;xg g55vmxwl gyf49dxa(cy6ed 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)zp*h0cnf9mr 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 + itj -iyj4bz*m )7hfnm +t5kj280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass m:g i8 iacw3tn(mg638gex8ib 7.3 kg and radius 9.0 cm rolls without slipping down a lane at 3.3 m(tgg:3 cex3n 8gwbii6i 88ma$m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as ther) 8ll tkte67d; :roe6nz7mf:ar ai f3 sum of two terf;f i6tdta7rne836e:rk l7zam o)l:r ms,
(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 m3h0qzk+ mcaxewq(x em* 2h* hj7q6cgqqtg5, 9ass of 1640 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate ofkmhw mqq2qx h7x5 q9ee+( gzaq ,306j gc*ch*t 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 5 037 ydwvldgtrest and rolls without slipping dtyv3 7dld0w5gown 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 verticalg* bpjr z(/dy(ly on its tip. It starts to fall and its lower end does not slip.g/rd* zy jb(p( What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotai bnlb jmk5 ;/d1zry 9vt,)e8c o1rpc.ting on the end of a thin string in a circle or1 m9ydv1 bc c;/r,tz i)kn ej5b8o.plf 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 cylindr:e3pdkid78y.:0 dg7uis z xh eical grinding wheel of radius 18 cm whep0i:.sekd3zg7u7 ded 8xhy i:n rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that is rotating at a ratewyyd+kmhmo/zb ,r 5 pva 6q 45h*nhv5g97 t)ui of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48 ) hh5m ,4y+6i9vzwy q5ptmo*/rhvkg u5and7 b, 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 moment of inertiysl7- zu,i4b ,gaois 9i3cu7aa by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position97caub-, 7zg ,sil4 ao ui3siy, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rots 8ah l*zrc9.goae2 d/ation rate from an initial rate of 1.0 rozhs2r9ec8 .l/dga*aev every 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 centerviwuo*3 yu.lox z3kods8 p62 l3ut78k 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. The dlz.po3lu8kw3t82u *v 6oios73yu xk 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 sfm n.dpl /z9ykw. 3ge0b6 /eikkater 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 momen :0qj 0 xtufmjh+qe1(pxy t6w3tum 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 inertia I is dropdqezw+8r-e3h - err)l ped onto an identical disk rotatingewdq)rr3z- hr-8+e le at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at)d r fb-+xd9aot7vp; v hjbbc,xsdq.1w;4l)h 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 standya .nkf3 +xr1c) 9ntiyc*e-ky s at the center of a rotating merry-go-round platform of radius 3.0 m and moment of inertia 920 1ay.ec n93y xr)n-t+yck kfi* $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely with an angular velocity of :j:hfn:pd (9m z.ptqp, oif6s0.8 hz:fo,.m p:6(:dpi jp ntqsf9 $rad/s$ 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 c/v*1f;-7:fm e4 leq0vsgea,iq :a kw8zyiucj ollapses into a white dwarf, losing about half its mass in the process, and wi,ujfeg0: klv-aqa mzy /fwv7i *eiceqs:8;4 1nding 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 1xj z1niv/s ;lwinds 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 xdd j07u vj82gzodv09$ 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 plat:r b(n a nhb6o8f t1utk51ftq,form, initially at rest, that can rotate freely without friction. The moment of inertia of thean,5:uf8b 1t ftn6 o(qhkbtr1 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 sta gza7 bvcvkwd/p74s/ 4nds at the edge of a 6.5-m diameter merry-go-round turntable that is4b /vdp4as w7kzcg/v7 mounted 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 ground with the end of the rope lying;eihrb/n d3ywj8 xzbc+15k5+ , zmg gi 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 doeb ixh ;k,wz5ndm+8ecijyrbzg+ /3g1 5s the spool’s center of mass move?

  The Moon orbits the Earth such that t(a)m7 j ,zmngdhe same side always faces the Earth. Determine the ratio of th)7j z ,g(nadmme 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.)    $\times10^{ -6}$

  A cyclist accelerates from rest at yzhv4l z,6bcmrpq,z/mm2z7 q yc. ,8ja 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 unifo )ruly3rml h+(rm 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 delivered by h )(+l l3umyrrthe motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 04r 2wans ,1hfq.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 reaches the end of its 1.0-m-long string, if it is released fromn w2 h,q1asfr4 rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of t)m-d+mk1e sh mf- na,xhe 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 4y8g )pyj)vu aour Sun, 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 neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the los))4 gva8yypjut mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is fo van3n 4bt)1kkr it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m ak4a1)knvtb n 3nd 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 an-d+mlt41jsd5 k.7 +t.cwg ay1qdcfoe $H_2O$ 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 itfuub ;h4 a+2at 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., weji* id+ )*4:f+h sx2zoxjcrrj 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 linzfco+j 2jji)xd: i+4*r *sx hrear 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 vertic8ltc)t+ unmh :gt i*.vyc 0b8bally on the floor, and we want to exert a horizontal force F at its axle so that it will clim)n b8i mh* vlc.:t8byt+g0ctu b 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 making8f; pc8/ ga(,zutkd8qu ) 7kmfago(mm a turn with a radius The forcedmt aao u8k;87fmpz, mg(gfu/(qc k8)s acting on the cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling of length 1.5 m and begins whirlftrvoz)rs 2e.;n6 dk *aq+.mking*r m.nzt+;v .ske62dakorq )f 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 come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thin rods, mes a p95ammbzr( mxc d1a(vka+ 31ds-8aking reasonable estimates +ddxc(rp3a z1v9e(8kaamsba sm-m15for 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 of two cylindric49q:n;7gb hph:6inwa rt9xm m al plates, of m:m7i 9nw h ph4;g b:n6m9xratqass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 Fig. 8 s)za o.7hk+co–58. What is the minimum value of the vertical h7 hcooskz a.)+eight h that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do notlm;qseu th bcza)s ,w/07;b3n assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutiomq4t6wttj,i1 5w n ey*ns as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diamete,ntqweymt i 4 j1t5w6*r 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