A bicycle odometer (which measures distance traveled) is atg6krin /.d40lukk+a v 3+ci o6dzk5kqtached near the wheel hub and is designedok6 5qc+nlia.ddk/ u0k+r 43kzgkv6 i for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular veloc5fd 7;sylcr3mity. Does a point on the rim have radial 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 lineal 5m7sc ;3yrdfr acceleration change?

Could a nonrigid body be described by a single67xow-t+j 6oe+ehg qi n be)8f value of the angular velocity $\omega$ Explain.

Can a small force ever exert 5i5edhl:sm y(a greater 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 don a;rew b3t2jkp; /s5o a sit-up with your hands behind your head than when your arms are stretched out p/s3;e r;2n t bwo5jkain front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at the a : q2f+.h*lgrsp,s4r *m gl8i0z6f7cdgjqqgpedal 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 *gqa*c m7 2s sg:6ljhil0rqg,. fp8+4qrdzfgsmall front sprocket or a large front sprocket? Why?

Mammals that depend on being able toicp/h5j)pb y: run fast have slender lower legs with flesh a: hyjpp/5b)cind muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry m m6 rjt)nv/p+r,;si ua long, narrow beam?

If the net force on a system is zero, i:u l h;siu6j;ny 9cb;qs the net torque also zero? If the net torque on aqly b6c ;;u9h ;jsi:un system is zero, is the net force zero?

Two inclines have the nas8rs; 55 mnri7zdyt (xk7 )9(kaklpsame height but make different angles with the horizontal. The same steel rlx(7dn5 7 k;mak 9n(isz8rs5k)ypat ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) downviahp8pqq i4+j : uotv( 02/rf:zk9qw an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has2q/jqpkw: (i8 zrq4+if0p:vo vt a9hu 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 samn5 6tlf9co o1tj t7e5im4cp-de mass. They start from rest at the top of an incline. Which reaches the bottom first? Whi 1ot- 6teoifct 5dl9p5 n74mjcch 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 momen yg9cvx284u xga*zi5 r17hhomw 2g*lftum are conserved. Yet most moving or rotating objects eventually slow down and stop. *w2h 2 x*zag9xv8cry4 o5il7mfhg u1gExplain.

If there were a great migration of people toward the Earth’s ezsw9p mw a.4cf(oe:n /csc1 )oquator, how would this affect o pwcom/4.(1s:z)9cs na f cwethe length of the day?

Can the diver of Fig. 8–29 do a somersault without having 6pp6+/d rkut )6jstxvany initial rotation when shu+x6j 6vsp rt/) kdp6te leaves the board?

The moment of inertia ofiqm3ozsonm:9 hdulf::rlv9 h7 . 5ik1xz h ;2a a rotating solid disk about an axis through its center vio:z2 qs9h 9 oa:knxrfm3;d .7hu5mz1: hlilof mass is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool hou qfd22f 5sk fzmp,7+slding a 2-kg mass in each outstretched hand. If you suddenly 7df5uq+ f,ms ps f2zk2drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identica)i7 fq9j *mitsl and have the same mass. However, one is hollow and the other is solid. Describe an experiment to determine which is whic7sjq ti)f*im 9h.

The angular velocity of a wheel rotating on a horizontal axle points wex,ue qfnyd4+1xp3w8 pt.hsk 0st. In what d,h8ey pfnktq + pwx .40s13uxdirection is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standtg1b7m,7 ze/8gu a au )i(ybp0 vrcy4a13wjising on the edge of a large freely rotating turntable. What happens us pie,18bwyabygi74cr(ujavm 03)z /7t1ag if you walk toward the center?

A shortstop may leap into th 2m(-ise byx0ve air to catch a ball and throw it quickly. As he throws the ball, the upper part of hi m2evy(b-xi 0ss 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 conm8epjlee++qw /kpl:k+gd3o2dj +u x1e2g+ jg servation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Dk +ge/+:dpd2 xgg +w q +8pj2l1ojjm +leeu3keiscuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following 2 1i vvubs*xq9angles 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 coincidencnv5c o2 re gsey4fd310e. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of t0n1gec3s y df2v54oerhe Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is direct: dodcg2;bkb 3ed at the Moon, 380,000 km from Earth. The beam diverges at abd dcb 2k3og;:n 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 motor is tu p2u(lilq kfd4flovq5u,0qe( 1e) ng)ghh3o+rned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the bla nfkh()(25hqpoq qfgegi+lv3u eod1l 4u)0l , des slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another gg;, 3/0 ewqua,s xkwlchild. If the ball makes 15.0 revolutions,w x;0,e gl /k,u3sgawq what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. ex el)5;peswix 4t0c;How many revolutions do the wheels makee ;xpi) t5s4xw0lce; e?    $rev$

  (a) A grinding wheel 0q;lnc2b)d n8d9v r :bh5k* dkh.35 m in diameter rotates at 2500 rpm. Calculate its angular velocindrd hl8k5qb dn;v92kb ):*c hty 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 revolubbe*+k/ t8 qxmtion in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m fxm/b+q8 k t*ebrom 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 4x59c,p umcf- o8gy st*rs)ovEarth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a poc9sobvfu7q0sp 5 )b-s int
(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 rotate if a particle ( 7na l 1chpu9h7hl;yr7.0 cm from the axis of rotation is to experience an 7unryl7 (hphc l19h;a acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerxoy-s gw/2aan;mm+b, ates uniformly about its center from 130 rpm to 280 rpm in 4.0 s. Determin;aa-m/bn +wmy,2g osxe
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radius m bvnm1:i x-;g$R_1$ 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 Apolqom;o jts;r t-tu 3)s-7jja0s o)av0ilo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no 0a mts utj; 3)oo -a7j-rqv0 tijsso);rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm in .- o;wmd7:( pjh+mndq 7rjhxd 220 s. Through how many revolutions did it turn in this mj7:jhho +n-qdw r p;d7(d.m xtime?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Calcula ixjwjxf4l3sa+ 95d+gte
(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 for0m0wtru bg/:( uuc v.o the stresses of flying highspeed jets in a whirling “human centrifuge,” which takes u/0 rov .ctw0(umgu:b1.0 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 x9c +ln b9.b1+plrj hfuniformly from 240 rpm to 360 rpm in 6.5 s. How far will a poinl19n+l.b pr9fxcbj+ h t on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 15003 vqxmq 9u3(ngy0j crepdx8 +p3 6k-kk revolutions beforg83c3k-y mxp60+rujkqnk3 xpe qvd9(e 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 unifokb3ibfs(- a/ brmly from 95km/h to 45km/h The tires have a diameter ob b/kf s-i3(abf 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 cay4vjb1lmxtp4y4 3zg, r reduces its speed uniformly from 95km/h to 45kmbzlx py4m34 ,4 gtyv1j/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weighk ayu5ty k9/-xt on each pedal when climbing a hill. The pedals rotatey5/kyu9axt- k 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 a1 -joszc nj(:kpw8 p6r door 74 cm wide. What is the magnitude of the torque if the force is exertedpp8js:6 w-(zj1okr cn
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel shown in Fig. 8–fbgzr*a0is ,t 9h(s 6d39. Assume that a rb09zs( 6gf ,dshati*friction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attachk.,46iphkv7eua5 bj sed 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. Calculat su45ap7ivk jh e6.,kbe the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require lv4p3+tqh,oetxgqgpl,zz e a)8 ,)qer u8( 8w tightening to a torque of 38 zrqt8t(qlp,v8q zlaeh u)g)e weo, x3p4g,+8$m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-kg sphere of radius 0.64-f,/ h0 8- o6xwqmzo+ngpwlat8 m when the axis of rotw ol- 6q ,8pnax +mf0hgw-toz/ation is through its center.    $kg \cdot m^2$

  Calculate the moment of ine;d24wl s/5)csqwf fn vrtia of a bicycle wheel 66.7 cm in diameter. The rim and tire have fvqw)/4 lfs; 5w2ncdsa combined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in a horizont)/fvb.gtn c5c al )nbt/c5c.fv g circle 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 ane- (*l6s m98nlrinx pigular speed (Fig. 8–42). The friction force epl(m l* r-9in6n8 xsibetween her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia ozty d0rt0 +f)tf the array of point objects shown in Fig. 8–43 about 0d fr ty+t)tz0
(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 ofae+p/ *ulu+8.h0 qal+fh janp 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 sqwcq yba2by7ube6wxgy) - 6zt+c1d*5/ e wgg; atellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required stea e;cbywww6ctgqy)xy*/qb- 1z+6ua 752b g dgedy 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 o ppoz:i.lcbq: m4 vfek,ynz9eht2 ). .f 8.50 cm and a mass of 0.580 kg. Calculate .2v z p :fzk9bh4qm). :,ole.ieptcny
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerating it fr4b* ( ahb5r)w8dtann ejlw a6(om 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 of 9)eqkee)tw qov6 /k4n a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque requik9wt q )/6 fkqeev)4eored to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut ofavbx3dp; i )g5u 7l/c9z7 smutf and is eventually brought uniformly to rest by a frictional torquec7vdmltis3 ap); u97xu 5zb/g 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 accelsfng8h 32i w(rl(q, qoerates 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 acti4)+ fphkfj,hcehy+ + con of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball i hch ++)fep+jk h4yc,fs 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 canwealfkp-k dtz /7;qg(ma6m 2 - be considered a long thin rod, as shown in Fig. 8–4lme mtk(72ag - /kqzafwp;d -66.
(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 massesvycons3/ 7 z)m*r3m fzs h:w*f, $m_1$ 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 fr ,fr -xrs7. fbl9npy(vom rest within four full turns (revolutions) anfbrl(py,f r-v 7s 9n.xd 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 moment0l8wv g1xiad; qm9ls , 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 developshtz 7 mq4dapj**;dn6vif eo -5 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 without slipping downo lu-.q jevv/hb1u70 :daz)uo a lan.u:oql1ouv)/ ja edvu70z hb -e at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the sum of3f kjqk 8s)z;k t kk8z3)qk;sfj wo terms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kd7w-btxm wz0ix.zk8x r )6b c:g and a radius of 7.50 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 it is a solid cylind w7c0x)bm-wz:rb ki z6dt.x8xer.    J

  A sphere of radius 20.0 cm and mgp:v b s.6u zc2:ttgagtx.n. 6ass 1.80 kg starts from rest and rolls without slippin .6tg t .6: s.zxactn:pvgg2ubg 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 on its tip. It starts to faf2le hcgfq,t4to- 6s9ll and its lowhc,oef26-t gf9q 4lster end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the end of mlt+t4wc yx08yw-h) oa thin string in a y mc04wxhto)+t-l y8wcircle of 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 cylindrical grinding wheel )wj3zap :mj7 dof radius 18 cm when ropz m)3jdj:wa7 tating 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.wc6ch mghevq- )89n o is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed c6.qwv chg) h9enm- 8oof 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 mo:yhbt b*m c,1ymq2a)sguu abi: h*i. 1ment of inertia by a factor of about 3.5 when chan *mym1s:, c tu*hq:2bag.u)1bihyaibging from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spiv-i9- ya8cgn nwn9/p tn rotation rate from an initial rate of 1.0 rev every 2.0 s tog8tnvc/ i-yapnn w9 9- 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(yaxpe1fd 6 hpu8v9 x) 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 thro9 ufy6 (xhd1p8e xpva)ws 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 mo y8d b1q: nr8fim wf0 oj7g8gzw8:qw+xmentum of a figure 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 Earthzf: fr v1p9 l89vsxj3p
(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 mom2ks8(em obh* oent of inertia I is dropped onto an identical disk rotating at angular speed kb(*eho2m o8s $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns awz3 iy. mnd,ue-p)4owt 2.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating+jamc tlbz- 7 -q25jae merry-go-round platform of radius 3.0 m and moment of inertia 92a- 2 t7blm+j qcaj5ez-0 $kg \cdot m^2$ 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 wi0u,ptcfpmr2 r g/k*.u27o zfsth an angular velocity of 0./*k0putc7s.ofmfr upz,r 2g2 8 $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a white dwarf, losing aboea1s4m izlf w lzt751,ut half its mass in the process, andml zszia4wfe1t, 1 5l7 winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in excess o 5o77tz 6h.tmhkoh(jnf 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 mc2 um81(b ww mnj-9ql$ 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 y4t5:o * vmaj2 2nbixjplatform, initially at rest, that can rotate freely without friction. The moment of inertia of the person plusx4ob2tnvj ij*y:m 25 a 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 diame68trm jv2x snrr.84nc ter merry-go-round turnts8 48ncjrnv2 r.xmrt6able that is 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 +p,mof 6 1pvifqsg4zi a q(.+fof the rope lying on the top edge of the spool. A person grabs the end of the r6z 4fpgo vf pa +s,iqm1(fiq+.ope 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 0vuoepq- ;ac:v;h1ns such that the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In thvaoup n;q :ec-1;h0vse latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rato 6yx 0q)-eyn. pre+vf 6a.)s;wug epfe 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 shap9loz2tvx;-w3zo ln k n.v;reom y*+f5e of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calkoo5 ovytl3v ; .-*;+ mx2n9zzflnwre culate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cyl zr ) ) 4lgwqjv5avmqv3*wl+:mindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it islqv+gjvmz ra) )l:wm* v5qw34 released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of/vvwh4cx.5jq8cq( v i the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 times as great, jtw);c/ffsczdt9f 0/ 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, losiw9f fc;0fd/j)ct z/tsng three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pouokw9+9oq st bjiyw s118m3 h*llution 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 a uniform cylindrical flywheel of dq9ios uojkw 8sm* w9113+bhytiameter 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 illustraxksjj17 7t )bltes an $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is k4)bdw,crb klt*z d 0ro9 qflk; l)k*0rolling 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.azs 58nf .6xl8 famd.r, we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally andmr.a 6la d88sz5fn .fx then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on thi)q1u,l.8seyfr7ft ee 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 1.8es)tl ,uyqi 7 reffheight h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is making a turn wit l vqs f4mwg93(gvzf7w,((t5ncplt ) eh a radius The forces acting on the tf et(p37 9cllq 4)s(nfmv5g,(g wzwvcyclist 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 ag +g ,r0jmqrl-6,jyz 0.50-kg rock into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is thejgm rzg ,ya0jr+ q-6,l 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 amm2a12kw d7 jtrms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outwd1t7m2maj k2stretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which con 2u3mq3pl ux3vsists of two cylindrical plates, of mau 2p xl33um3qvss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 track7ma r4sq g2:yt9 fg8kg of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of th:s 9krtm7 48ay2gf qgge loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, butwm -b vlsb l7*2)((j7t:iljkei(e g mj do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as th7c sbkbu7 s8m4e car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0 b4b 7ssmk87uc.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