A bicycle odometer (which measures distance traveled) is attached near the whe0uzqys.6 ra2yn2 ne r k.bm4;wel hub and is designan n6 wr.ybr.me;kqz0s22y4ued for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates ac1f3pyifop 36t constant angular velocity. Does a point on the rim have radialpcf31pf6 yi o3 and/or tangential acceleration? If the disk’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 described by a single value of the angular velocd)ie/9 j tdh zgjq7gcf5dsw2tu.um ,i5* 7ac. ity $\omega$ Explain.

Can a small force ever exert a grptr :* v+m d9knimiw+purm,84 eater torque than a larger force? Explain.

If a force $\vec{F}$ acts on an object such that its lever arm is zero, does it have any effect on the object’s motion? Explain.

Why is it more difficult to do a sit-up with youru ,0nc5x y ex-4zdk* h0 zzx 8bjvw9pz-6cx;oa hands behind your head than when your arms are stretched out in front of you? A diagram0pvcx cex k z 6d u-zzh;nx4,xjo-w*z5b0a98 y may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at the p 66 8l. 2zcqllcmhfk.bedal cranks. In which gear is it harder to pedal, a small rear sprocket or a larg8lkzlb 2hfml c .6cq6.e rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slbwet zv2er2h*qw b o77 ea76v;ender lower legs with flesh and muscle concentrated high, close to the*ezq7wat2obv7ve76 e w b2rh ; body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkpxb2lx,ls:r j)k 8ob 4ers (Fig. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is gxxo blv;2j 1qj178q lhxg.n, the net torque also zero? If the net torque on a syste;lg 7gbnvj xlxq211jq ,xoh.8m is zero, is the net force zero?

Two inclines have the same height but make difs,ges 0dk)xj6) gn4hm6 d u 2m yt8np90czuwv)ferent 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 be greater? Explainv9uyp)z2gt4ds0n cx me w gh60du )kj,86 nm)s.

Two solid spheres simultaneously bs4x+bxw)w f /start 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 greateswx4+ bw b/xf)r total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and(xvw.da o-n.j the same mass. They start from .n-v. odw(axjrest 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 rotational KE?

We claim that momentum and angular momentum are conserved. Yet most movingv2 l0hnb3sa 2(cvn nm9 or rotating objects eve(9vvln30 c s22bnh namntually slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equa+:jed;:iwji /yt1;ao 2lpj uator, how would this affect the2;/a:jtjuoyp ; :id1wela+j i length of the day?

Can the diver of Fig. 8–29 do a somersault without having any initial rotationerbn h9foa +1 ewg 55c 18;bdvw(,subt when she leaves 5eu o,a(1bh5er+1 s fwt89w;bgcnb vdthe board?

The moment of inertia of a r1ty ky8.of i7sotating solid disk about an axis through its center of ma kis oy.y18tf7ss 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 sto nk1)zktkhlh czql5(z zc*-.t ,p; h:pol holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decreaseqk )ktz5pn;1 zzhk (lzhp *-.h:,ltcc, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is holgsaj nxb9z+taa:qm- 5qm)m* 5esw7/c low and the other is soli5 q+ w:bsan7 jx9t-gm q)zm5/sa*am ecd. Describe an experiment to determine which is which.

The angular velocity of a wheel rokzwh90c ;9egr f yq75rtating on a horizontal 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;9erh5qr zk 97yc0gw f acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edgiw gfyle08ze8fk9qqzo9+,:vb3za;jt; mc7qe of a large freely rotating turntable. What happens if youezyq:, cb;qz9ke z7jv l gf9wt83o8+;i amq0f walk toward the center?

A shortstop may leap into the al;vfy e2orc47rss b, f/vp q16ir to catch a ball and throw it quickly. As he throws the ball, the upper part of hib;qc,fr1ov2 r6sve7pf4l s/ys body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular n*s ),t xwpe 3kjj2u;++dbqkv momentum, discuss why a helicopter must have more thq+eunvk2 s*,xb)3tdj k;+ wpjan one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in ra0dnvqjz4e+ dgo;u: :kdians: (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 o3sf vdiq ibo()(4cr1r ds, c(bf an amazing coincidence. Calculate, using the inffdv34 c((isqb1oibr(s,rd c)ormation inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam diverge981 3pvob zqvjs at anp1o 9qv3jvbz8 angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. When the motorl5+(g ej kmqxx )f-8zqou :7c:ndo+ xc is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades :jqn:x lm-xogc d+e5zcuq8 kf)ox+(7slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another j01rya1.i(fg thqc0j hj lfb,gr07;hchild. If the ball makes 15.0 revolutions, what is its dialthg y,0f;fjcjgrq01(a ri.h 7hb1 0jmeter?    m

  A bicycle with tires 68 cm in diameter :hb6- 7nyiqk ky4, sjxtravels 8.0 km. How many revolutions do the whijxq,h bykynk :7 -s46eels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate its angulyw rdvz ov0/sf g:mdy/ 5.o8)ogt-uz/ar velocityvmzuo.o0/8sft/ )-rg5vzyywd:g /do 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 in 7szmc))z nzp +4.0 s (Fig. 8–38). (a) What is the linear speed of a child sea+z c)z)z7nmsp ted 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 ar2qtd +lb-y)3ivobvu 6ound the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed ln:/;yncn j+bq ) 6*xqjxft 8pof 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 centrwsba67 4qc7(3 cutsgwifuge rotate if a particle 7.0 cm from the axis of rotatitw3 qu basscc67 4g7(won is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly s. s:s 9tuhnt2ic3 zy81jyi8 kabout its center from 130 rpm to 280 rpm9z8t kys tsy:1ij u.sh3i28nc in 4.0 s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radiusy4srz* bq0j32dq q 3zs $R_1$ 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 aboa:*+s0 ek;ykqu,aia m0 xa+ vkmi3ae7yrd the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time i 0;7 0x ska muiaeviqy*ma+e3 +y:kk,anterval. 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 15,00-c ,7x oqrhp809llyd h0 rpm in 220 s. Through how many revolutions did it ll8d 7 q-0c9h rxyho,pturn in this time?    $rev$

  An automobile engine slows down ahz53iwul- x wa7w8t,w 6w.jbfrom 4500 rpm to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jets in a who-sii. h(gs,z/q7m ms irling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching itsgq (m/-o s,im.z7 sish 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 tocz smll576+bznm 6 h0(mgn/i s 360 rpm in 6.5 s. How far will lmn/7(m szzhc5 gi06nb +m l6sa point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off2ja nv i uv41nu99j(xbi:du)g when it is running at 850rev/min It turns 1500 revolutions befor)i4u:v a1vn 2bjjgx(ndu 99iue 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 its speed unifo0/m oe8ax5k fdzg -ng-rmly from 95km/h to 45km/h The tires have a diameter of 0gfaz8o -0 emkx/d 5n-g.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 reducesz3wiwd)n 9 /w* vpyvn* its speed uniformly from 95km/h to 45km/h The tires havvp9y iw nw)n zwv3d*/*e 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 cles 28*bg 1qzcsimbing a hill. The pedals rotq c*1zegbs2s8ate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 746fv h3z-)ebiqx) fts( j;toe - cm wide. What is the magnitude of the torque if the ztq jf )6-;hb(v se3eitf)ox -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 4*a wg2wem6p nof the wheel shown in Fig. 8–39. Assume that a friction twa 6g 42wmnep*orque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a massless sgv0o-5l48g2(1 ntvycata ofrod which pivots as shown s5yg(2vt vo4af lao-1tnc8g0 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 h lw*1zb6jo- zy3kd2;u5tmc iof an engine require tightening to a torque of 38 lmhwkj3-dzc u*5o1bi;zy26 t $m \cdot N$ 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 sphs:*(d m17) sjs8buvqw6vt3 dfqkl5xu ere of radius 0.648 m when the axis of rotation is through its c8uvs6dwdfb3q7 k(stul) xqs *j 5m v:1enter.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diame*0g54gvceq;nkof y a5d.*amzter. The rim and tire hayagd.em4qf a g 5k*oc5 v;0z*nve 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 noco x8z..:qmp2aj8 hon the end of a thin, light rod is rotated in a horizontal circlpx8o8:z chmn.2.o jaqe 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 andzq:2o ywcvkz;k9e( hk- zq40h(mt*rgular speed (Fig. 8–42). The(erq kz yzkh2q(doz wvc 09;mt-h*4:k friction 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 inerti ie*eft/.hm9l(zift-o wh a2 3a of the array of point objects shown in Fig. 8–43 abouat/ -l( zf3toehwi.f h2e* im9t
(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 consia2 aech9s/t) ists 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, unifonmk9cg8 j8ge4rm cylindrical satellite spinning at the correct rate, engineers fire four tangem4g en gkc988jntial rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a ul9aq 7 yp4+z ,7zzcdnwniform cylinder with a radius of 8.50 cm and a mass of 0.580 kg. Ca 7+ dpz7zna,4y9wzlqc lculate
(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 swinywa vx/ /(kb:bgs 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-driven mep8xjw d;c(vbxf t15e b .7p1efrry-go-round and is able to accelerate it from restf(bdej pvf5ex7.cxw8 t11;pb 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 torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotatijjq3+na- doa;ng at 10,300 rpm is shut off and is eventually brought uniformly tj;j qa-ao3+ndo rest by a frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a 3.6-kg t/. ilqt5w4la1k(5rk ie:o lf 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 forearmauzngqq7p6ua 89/dd* , which rotates about thq9d*aq 8u up6/and7gz e elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thin rod, as showmgvv9w u6(3ryn in Fig. 8–4(wy6v93rgmv u6.
(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 mdm/t5 p ,bh1;)ned7uk3bq mbof 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 (revoy7c6z/1t,o hq/wp tq klutions) and releases o6tc qy7 t,z/ /hkpw1qit 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 momenzu: 2nj c -r.jlt5q0nvpa7xj,t of inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develh.yb(*noa p)0 -x ytok/wx u9uops a torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls witho:d5xx p:gor7tut slipping down a lan dpo5x:r t:g7xe at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with resp d(+9(gs1 vus zpjk:xqect to the Sun as the sum of two tvg (9 xs sdkq+j1z(p:uerms,
(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 gn9 h e blp68ly:4n:nh7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume iy6:l:g4 bh 9npen8nlht is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest afr9 (68zkoz du*, puk2 vpo-qvnd rolls without slipping dowr(2 vvo9k-8fzpqp*zuo k du6,n a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

  Two masses, $m_1$ = 18 kg and $m_2$ = 26.5 kg are connected by a rope that hangs over a pulley (as in Fig. 8–47). The pulley is a uniform cylinder of radius 0.260 m and mass 7.50 kg. Initially, is on the ground and $m_2$ rests 3.00 m above the ground. If the system is now released, use conservation of energy to determine the speed of $m_2$ just before it strikes the ground. Assume the pulley is frictionless.    $m/s$

  A 2.30-m-long pole is balanced vertically on its tip. It starts to fall anlmhab2xau od),a1 8 y*d its lower end dola )u2a m,*1a hyd8boxes not slip. 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 momeu4n-9gb pbg02l g ,fkontum of a 0.210-kg ball rotating on the end of a thin string in a circle of ra g240g,uboplfg k n9b-dius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentu0l:mm2xd.n xfm of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating.x2dxm nmf l:0 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 4aewg (/e rw24ehtsf,is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position,4et,2gewfh(4/re s aw Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can reduce her momyi 5sd70/zsrg )z. utuent of inertia by zszdt7g.5sr )iy0/uua factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can incre9,yax5rq m5c nase her spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a finalaq 5rn5 9,xmcy 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 tha)kj24 do3ej brough 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 of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotejboj)d2a 3 4kating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a f,hhme+,kxwn r. : b6kk juvh,+igure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of the Eart2eg yd1.azzqa kt 5l*8h
(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 88oy:9 gk e+t)y aqntn,7 v.n5prntszinertia I is dropped onto an identical disk rotating at angular snnyz8 tey t .pto5a 79n8n,s :vr)gqk+peed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.y qr12)o2 gyjh4 $rev/s$ 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//d b ze20/ fhvkniweyq+8 ;bx platform of radius 3.0 m e8widx+nebb20;/q // fhykzv 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 rot+*e)t(uhts kx ating freely with an angular velocity of 0.8 )ut (x*eskht+$rad/s$ 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 colll,h6n6o j6sz ieppu b+/+ijtrtw 3-2e apses into a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing rado3 +s,hjpt /rwi l6z66jpu- ei be+2tnius. 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 involdnq :*vx3cr qgo.)i* ive winds in excess of 120 $km/h$ at the outer edge. Make a crude estimate of
(a) the energy,    $ \times10^{16 }$ J
(b) the angular momentum, of such a hurricane, approximating it as a rigidly rotating uniform cylinder of air (density 1.3 $kg \cdot m^2$) of radius 100 km and height 4.0 km.    $ \times10^{20 }$ $kg \cdot m^2$

  An asteroid of mass z iy 3+f9: jkhxp79iom$ 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 ro;yg-n pkj8kb6m b ngo9qq8. 5ptate freely without friction. The moment of inertia of thmkn pp.jbb6n8k9 85 gq- qgy;oe person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m diameter merry-go-round az :qd/*ty pr c6,uvy;)5w/u+ecwldpturntable that is mounted on frictionless bearings and has a moment of inertia of 170dp l*5uyqzw,ut)ce/:;+ /ap ywv6cr d0 $kg \cdot m^2$ 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 onch-1.go3ct dv7f(lsl the top edge of the spool. A person grabs the end of the rope and walks a do( s.cd-71vf3g llthc istance 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 Eartqf1/ g+jd7p3*nnl wk9caxtz 0h. Determine the ratio of the Moon’s spin angular momentum (about itp 7cx9*j w1 lfnzqn 0tkad3+/gs 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 fe;ih0 l2 fdfx 2l7lov-rom 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 0.20 m acq( wk-c3noyfg3uires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the mo ny(co-3gw3fktor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each owbt b8/(n 4yr-;tzizm f mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yy;(ntr i8 -tbz4 /wmbzo-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)tfux-zeb :0vq jo bl,g,s1do 4c 5sq. ($\omega_R$) 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,p.bu7zt ;*1 izf rs0my 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 sm.utzr1 py* 7fbzi;0 be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use e7 3pbdz)bgh u4 1z0votnergy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel ofpzg 74vbbot 1z)3ud 0h 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 agn3 j gjdm;z)z 9vtd13n $H_2O$ 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 abof,g7 gr.ku8( km8u on a horizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (i.e., we ignore frizft o6nvf0:1slf+te:ction) 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 accel: z6fff1oe+s tl:0vnt eration 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. I5ao/e4;crr mg t is standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step has height h, wherer5ro mc /ea;g4 h

  A bicyclist traveling with speed v=4.2m/s on a flat rjpthy ln82i- 0oad is making a turn with a radius The forces acting on the cyclist and cycle a0-nl2ij p 8tyhre 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 w wgz.b+jxi+ffhg9d + 5hirling 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 t .ffd9bg5z++hw+jx igo achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’d/ ktw rb3iy).s body as a 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 skater withwdb3ik)ry/t . outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical plates, oze iz65r+qlum5z k,,if mml+q, iezikz55r u,z6 ass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 th 8-idq;4wg8oa 9kv cbqe looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must dro-qoa8b 8;dgqi 4w 9kvcp 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 d )(z w upvss nkqom05:u8n;q;ro not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the bhisso:cfvg:d,6r.,( xc zm*5 gd g:dcar reduces its speed uniformly from 90km/h to 60km/h The tires havedi:sfo* .hgv::6cgr, x(cbd z,g md s5 a diameter of 0.90 m. (a) What was the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s