A bicycle odometer (which m48k vzglf :-fneasures distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-in- gv8fzl4n:kf ch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on the r)lhj zto(dx, km;x:/1ea+pqw im have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the hwzt)q1+jem,kx pl:/(od;x apoint have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single val)eus fr ;) 5qv5vn;mzzm2dz1 pue of the angular velocity $\omega$ Explain.

Can a small force ever exert a greati 6zm+ctji:ln 82;6vk ; oub tubu4aoum8k1c0er torque than a larger force? Explain.

If a force $\overrightarrow{F}$ 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 behind your c+cq 8,:bkdm.;xqoz bhead than when your arms are stretched out in front of you? A diagram may help you to answedzc +k 8 xboc.q:bmq,;r this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at the pedam+asx7 (fa*b0nh:a/j y wad0,ozg) oi l 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 lo+ma*: oa0,dif)n 7aa/hg sxb 0zyjw (arge front sprocket? Why?

Mammals that depend on being able to run fast h pjx (ht4satz:30 :veiave slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis ofthszejvt x(:43p a:i0 rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a lonb0hgkm7,bkcpg;p fz .93 / uong, narrow beam?

If the net force on a sg1fvo) +ocaz.u0ig. c ystem is zero, is the net torque also zero? If the net torque on a system is zero, is the net force i co+a.0gzcv)u. f1go zero?

Two inclines have the same height but make jnw x- 1+uikk+ipm -wi1qez18different angles with the horizontal. The same steel ball is rolled down each incline. On emkw1q1wupxn zj-kii1 -8+i+which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an i o*adi6k2v c-u)jy4 sbncline. 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? Whiayk)6j-v*cois u42 bd ch has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They s+ im .qrnx/o846gryv/ iyey )start from rest at the tsyox4i/givnyem / q86r.y)+ rop 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 rotational KE?

We claim that momentum and angular momentum are conserved. Yet,v w( /,eyikkgx9twv tgq0cw /1dsl; 1 most moving or rotating objects eventually slow dow1ikvy,/ ,q /t0t 1w9 g les(wkg;dwxcvn and stop. Explain.

If there were a great migration of people toward the Earth’s equator, how),wq f *d3ni;ntir/uj would this affecq*dn3/ ni ) r;j,wuftit the length of the day?

Can the diver of Fig. 8–29 do a somersault f rvdx4gut-htgr( *98clpv05without having any initial rotation wht8(gvpf5h 40*9u v rg-dcxltren she leaves the board?

The moment of inertia of a rotating solid disk absym c,qbju5mlr q;+0taak1s91;x p4nout an axis through its center of massy;p q9qn+sjmkcb,5lat x r0s4 1a;um1 is $\frac{1}{2}W{R}^2$ (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 outstrc,twxpno 0e77etched han on7cxe0t pw,7d. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the samta00+igyr+hb i8mw*2sq izl-e mass. However, one is hollow and the other +wrlti* z2 0q 0aiy-hsmg b8i+is solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle pointnsdj+ kaq *e39vbu- iy8 p o5tk-5bad,s west. In what direction is the linear velocity of a point on the top of the8v-9 epub*da+, nqs bko5akj3d-yt i5 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 increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating turntable.g fey/qnanqsn9ocm i3z8805l0w 9 y;j What happens ns0ci3 5oe j8 9fw8 ql/;gany 0zym9qnif you walk toward the center?

A shortstop may leap into the air to catch a ball and throw it quickly. As he t:wyl m. p uxnofrg99,u; y.5nlhrows the ball, the upper part of his body rotates. If you look quickly you will notice that .ynx glyp 9nlu.95 :f ro;wm,uhis hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conse*a :k*19fvqlnfftw06 owqju 1rvation of angular momentum, discuss why a helicopter must have more than one :j aku691 ftwo10*q fvf*nlqwrotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles a+i0z o gb.vk;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 w.x j.yy1l+aa coincidence. Calculate, using the information inside the Front Cover, the ang a .xlayj+1yw.ular 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,i5ilaqk 3s n k bbys1ta;9+./z 380,000 km from Earth. The beam diverges atbs1/tki azalky sib.5+9;q n 3 an angle $\theta$ (Fig. 8–37) of $1.4\times {10}^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a r,pzalm,a( 0te ate of 6500 rpm. When the motor is turned off during operation, the m,(,t0laezp ablades slow to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If the ball m q14zm;q,rr--eh7le g abm4ilj ey4k:akes 15.0 reb4-rhmqi mzqjyl7k :;e- rg414eae l, volutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revol 09fiv 6/q yo(;izkumyutions do the wheel yz(qv;0 yk /imo6fui9s make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm.q qz;y7pp0 ni4 Calculate its angular vqp07n; iy4zqp elocity 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 revolutiofpxgzu q8 /u:)n in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m from the cente q/fx 8)g:uupzr?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular veloc.w8.dgl ck :jp3k*ow2cuk ut4ity of the Earth (a) in its orbit around the Sun    $\times {10}^{-7}$ $rad/s$
(b) about its axis.    $\times {10}^{-5}$ $rad/s$

  What is the linear speed of a pointuryv/n1v fc1:
(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 rotd:rlvu +ehi+; ate if a particle 7.0 cm from the axis of rotation is to experience a h rue+:li;v+dn acceleration of 100,000 $g^{\prime }s$?    $rpm$

  A 70-cm-diameter wheel accelerates unif0p7 ki d2)yr nowg7n1wormly about its center from 130 rpm to 280 rpm in1o)2kdng yp r 7i70wnw 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 radiut- , *a;9mrl2bdezlghs $R_1$ 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 spacec0(lajoky.,7 ( ldcopt+ap:lor b./sgraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revo /bl aa( .j0rgc7l,po(.+ts ody ol:kplution 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. $a_{tan}$ =    $\times {10}^{-4}$ $m/s^2$ $a_{rad}$ =    $\times {10}^{-3}$ $m/s^2$

  A centrifuge accelerates c1 m k*ct,px7duniformly from rest to 15,000 rpm in 220 s. Through how*ctcp7km1 d x, many revolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm inb2xd3b8hcblbi4v- af 4 g92je 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 for the stresses of flying highspeed jets in a whirlildypk wn4du53 ,kyf9umm,h2- ng “human centrifuge,” which takes 1.0 min to turn through 20 complete revomdn2fkhpw,lud 5ky y3-4m9,ulutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/mi{n}^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 rpm to 360 rpm in otu)7 zx8ac1e/siws4 6.5 s. How far will a point on the edge of the wheel have traveled in tht74eas/ix o)zc1 w8us is time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 150 fup.eee7)5r8jw5x., aa*yr0x rmi gm0 revolutions before i*0 irjm857px)ua.ee ,rf5 ymxa.egwr t 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 its speehvuxd8u qm 9y9 /*/tvud uniformly from 95km/h to 45km/h The tires hav xdu9 uv*8yq/ vh9/tmue 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 a e)n- r vj1.hlsdc *uc:+cy4h65 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a sl1h)cac4ed jn*+ yv.ch-:ru 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 ped,k slmg5p2,yval when climbing a hill. The pedals rotate ivk,pl5 m,y2 gsn 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 74 cm wide. Whhlx.y1/k 4 he1cb k59 vijuhbhc4-x;uat is the magnitude of the torque if the force is exertejk5l1c1 ;xibh4khh-u/c.v uxh4e yb9 d
(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 wu+ xjje-3 r*ltheel shown in Fig. 8–39. Assume that a friction torque of 0.4xjlu rej-t*+ 3 $m\cdot N$ opposes the motion.    $m\cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a masslesumrlc uwq0o7c;7 + 3 wv0*diuus rod which pivots aswu*r0luu7cu+30d qo vw 7imc ; shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine recy.i7bq2 auox4-)orrwrt0f+ quire tightening to a torque of 38 -)7 u+wocoi4t2xr fbrrq0y .a$m\cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-kg sphere of rg542g9uxq bfipqjo9 ;adius 0.648 m when the axis of rotation is through its jx29i4up5fq;qog g 9 bcenter.    $kg\cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 665og6,g8c vjfy .7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of thejo 5gvycfg 6,8 hub 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 horizontagnu k(os de)jn .z+b:kw:,2hol circle of radius 1.2 m. Cal:eukh obj gs+d (:n wzk.)on,2culate
(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 constantjq( 0.kdnfey5- -zoy0 mqq,g q angular speed (Fig. 8–42). The friction force between her hands and the clay is 1. mq0jeqqkn-o,fq0 yy5z(d -g.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 shownn1bozja/ i67:; utxy)1pw/xyhbv ) pp in Fig. 8–43 abo/uho1p p17 b/yxbvy)a wni)x p6z:;tjut
(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 is sm yg .y.op1mp3y-. aaqec0b1 $5.3\times {10}^{-26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $1.9\times {10}^{-46}$ $kg\cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times {10}^{-10}$ m

  To get a flat, uniform cylindrical satellite spinning at the ezx ;pb l)7y2e6fe3vwcorrect rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a maswl e7)yvx23 zfbp;6ees 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 yuu+ ,/ dv9rae8.50 cm and a mass of 0.58d+u/9a , rueyv0 kg. 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 swixp840 sle +wes+++rgpeer8 n( c c:tcangs a bat, accelerating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m\cdot N$

  A teenager pushes tangentially on a small hand-d482ce nc.pnhaq l :d.oriven 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-roue8pc..2alq:n4hc dno nd 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 r,iabd:hciv4n 0 pt0egoe *v44pm is shut off and is eventually brought uniformly to rest by a frictional torque of 1.p4i4eb04*0intc :o,ve dg vh a2 $m\cdot N$ 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 ac/ott dl6b,7n hcelerates a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m\cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action of the forearm, whi lg:f0, zuruv0fxy .k+ch rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The +zkr u:,0vlf.xy ugf0 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 lon fwn(s9gxxfyzc17+ xa.i8hj 41uzi+ lg thin rod, as shown in Fig. 8–4 u49if.sl+8yx17 hifj xna+(x 1gczwz6.
(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 ofpkw2*q7rfn e. 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 accelerate:k ;)wmamwn trv5*)kai9se7 us the hammer from rest within four full turns (revolutions) and releases it at a :at95ksk)m*m; v7ri wu)a ewnspeed 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 inertiar 0c(* nz)y6vdt r fk)uflv,,m of $3.75\times {10}^{-2}$ $kg\cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque of 280f d7rwytjnc7/o3sq50cx n8:q $m\cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 k4u sdh1g z-61nahk5l vg and radius 9.0 cm rolls without slipping down a lan 6-1uva4hl 1hgkzd 5sne at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as thapvnmv.,y;j,t: p j)me sum of two term pyptn,;:mvm.v jaj) ,s,
(a) that due to its daily rotation about its axis,$K{E}_{daily}$=    $\times {10}^{29}$ J
(b) that due to its yearly revolution about the Sun. $K{E}_{yearly}$+    $\times {10}^{33}$ J [Assume the Earth is a uniform sphere with $6\times {10}^{24}$ kg and $6.4\times {10}^6$ m and is $1.5\times {10}^8$ km from the Sun.]$K{E}_{daily}$ + $K{E}_{yearly}$ =    $\times {10}^{33}$ J

  A merry-go-round has a mass of 1640 xr4/qvqcr5;ky wn2 5bkg and a radius of 7.50 m. How much net work is required to accele;5k wq/rb 2vxrycn4 5qrate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg sta/ or9/8v6z xtv6ab)f-bkh mizvs2ge .rts from rest and rolls without slippingm- 6vv g68k/o)b9e rvtf x/2 sz.bahzi 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 vertically urk3 6cva+awuy202jk 1-c syj 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 by20ac 2uyc+ 6ur1j-k wkvjsa3efore it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the end of a t/k9mmt c9 oko.hin string in a circle of radius 1.10 m at9.tmoco /mk 9k an angular speed of 10.4 $rad/s$?    $kg\cdot m^2$

  (a) What is the angular momentum of a 2.8-kg unif+jv fkhr9 xd80orm cylindrical grinding wheel of radius 18 cm when rotating at 19+x j8kdrfh v0500 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 zhjr8jha- mo/rb.-j,3 wt as ,j4dd, fce4 yy8his 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 -/a j.fca,, hos4rh dyj-be8, 3t yzw4jrmjd8speed 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 ig8r/ f6:/s eny hwcht7nertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations r w6:/tg y/87heshcnf 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 z zu0w16,lygdga 6 osn80uf9d initial rate of 1.0 rev every 2.108 ud f9zzga0 uwygols6,nd60 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 verticaarqb ,i (4mxf-p)ip-i l 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 0.40 m. The potter then throws a 3.1-kg chunk ofp xbpm-(f- i4qr, )aii 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 ;z/rb5lz sz) yooh*g -bjx,j2spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg\cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m\cdot N$

  Determine the angular momentum of the 2z7wx lit;8asEarth
(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.    $\times {10}^{40}kg\cdot m^2$

A nonrotating cylindrical disk of moment of inertia I is dropped onto an idenk9lis9m s,icb4c5:6+jbvfl xtical disk rotating at angular ici9ls9,54vm xb 6+j:bfclsk speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 24kw c,s/4p v)it;o/lk2ua rha .4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating merry-go-round pla 9w5eieux0hs y4z-e o:tformewe04-z iox59s e:uhy of 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.$K{E}_i$ =    J $K{E}_f$ =    J

  A 4.2-m-diameter merry-go-roun fd5(q1dj+vw:v fef;gd is rotating freely with an angular velocity of 0.8(+1ddqj 5fv; egv fwf: $rad/s$ 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 eventuaxh+yxye p4 .2z)aquz,lx7/ wrlly collapses into a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assumingue4 +a)z, pyl.zxhxq /7xyw r2 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?$K{E}_f$=    $K{E}_i$

  Hurricanes can involve winds in excessdd,c 2( p6yc12 j gzg3jrzxjr7 of 120 $km/h$ at the outer edge. Make a crude estimate of
(a) the energy,    $\times {10}^{16}$ 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.    $\times {10}^{20}$ $kg\cdot m^2$

  An asteroid of mass :htj7 uy wnl/n ou0g57$1.0\times {10}^5$ 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.    $\times {10}^{-16}$ %

A person stands on a platform, initially at rest, za6lc 6q1u7vwj yjc;.that can rotate freely without friction. zyjcl6qjv.awc 17 u;6The moment of inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity ${\omega }_W$ What will be the angular velocity ${\omega }_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will ${\omega }_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-mu7;eyd7(up 0m y5m6sbbw2r iv.vjv l / diameter merry-go-round turntable that is y(0;dwurmjvvu7p e7ib ./l 5 yb2v 6smmounted 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 ec (83.ktrq/f9 qmwvpo nd of the rope lying on the top edge of the spool. A person grabs the en8vr(qq.mk c9tf po3/wd of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always faces the Eartmbk.ru+u)ptp qnuet,n 6t- h - 0(+zuxh. 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 orb.0mnuupt+qp- +x-u ke)(6t,bhutzn riting the Earth.)    $\times {10}^{-6}$

  A cyclist accelerates frota fap5 rw ycqo9c 38ns)66xk6m rest at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of radius 4mis e1:o2 eyc0.20 m acquires a rotational rate of f 1e2ey:os4cmirom rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m\cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, eac-s2ni 8vto/v i9k-ntzh of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0i -s9z/ totvkvn2n-8i050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the rear wheel c0/(m opw3:ecbcv 8ib(${\omega }_R$) 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 mas2 c /6 .upgqd-oj+bmlzs 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? Assp j bl2.qm6/cgdo+z-u ume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times {10}^9$ $rev/day$

  One possibility for a low-pofkv ,x8s 9(i ezql pl:.ol,(pmllution automobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses oplm el:x l,zivf9 ps q(,(.k8a 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 $1.7\times {10}^8$J.    $\times {10}^8$ 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