A bicycle odometer (which measures distance traveled) is attaww/o6*k dv k6hs7e jopp+p wc/6e 5xg9ched near the wheel hub and is desig69kw/7*goxedp+ pw pehwvc/s566j ok ned for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on the rim havhy pqw gc365zki p:qml:8)d;q e radial and/or tangential acceleration? If the disk’s angular velw qzpkp :gi8c m:5 6d;yqh)3lqocity 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 ve7qn7 sjn dj:n c+l0p2mlocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger forceb: pi6gjy-whfg5 w zy ,jqs.8+? 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 difficult4hb hs;: peg+)sxacmc4 j ;q6m to do a sit-up with your hands behind your head than when your arms are stretched out in front of you? A diagram m x p;sb4sh: hcqe+6c4jm);agm ay help you to answer this.

A 21-speed bicycle has seven s2m aca1y5 n*cp(8cajfb;c c1sprockets at the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a smycjpa821;c b 1acfa5mc (n *scall rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run faso0 6 hoqt231 :o0/ excps2nrkloy*svz t have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). o:k0*y xlqts6ze20hn1ospvr3c/o o2On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers ld0hbxvg )f 1v 2(hks5(Fig. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is tj 7,o+yul 9x 1vo pm9+5lkucowhe net torque also zero? If the net torque on a syspuu1vl7cmyx9owlo 5 +j +9ko,tem is zero, is the net force zero?

Two inclines have the same height but ma k6fpio 3/mzl)ke different 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? 6m lk3pzofi/)Explain.

Two solid spheres simultaneously start ro3rzg z;.z (ngllling (from rest) down an incline. One sphere has twice t zzz.(l;g rgn3he radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. Tht2gkkulwc5 6c gz+ z, :u:) qzbrghl4.ey start from rest at the top of an incline. Which rea2uzz5ck4kwh.lz), g c r+u 6:q:btlg gches 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. Ye3y6tp2 uew bm9t most moving or ro9e m263wybut ptating objects eventually slow down and stop. Explain.

If there were a great migration of people toward htny:ge-2i; xp651vz i lm y2ythe Earth’s equator, how would this affect the lzgh1px v2ii6:y -lem5y ;yt2 nength of the day?

Can the diver of Fig. 8–29 do a somersault without havin33 .7y, rc:g0fc svqk axo3bcqg any initial rotation when she leaves the bo 33q7 bgxc:y rk,a3 o.cvqs0fcard?

The moment of inertia of a rotatin.*l- w.rymmyi g solid disk about an axis through its center of mass ism.l -y.*i rywm $\frac{1}{2}WR^2$ (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 rotating7 dpo /l but0t,yu1nu1 x )0fxbt3h,vp stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular vexnbu uu,o7d/t1)ftb,h1p py xt03 0 vllocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. Howew;oc-os a2prtu 6p-v 3ver, one is hollow and the other is solid. Describe an exvw2u- opa;to3 s cpr6-periment to determine which is which.

The angular velocity of a wheel rotating on a horizontaw 0l1c7b+pkyt l axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?0cbytk pl 1w+7

Suppose you are standing on the edge of a large freevoy3 dz )0xap-ly rotating turntable. What happens if you walk toward the centerx v ydz0)pa-3o?

A shortstop may leap into the air to catch a ball v- xrcqr,fs drk/-0 *qand throw it quickly. As he throws the ball, the upper part ovs0-kr/* q f,qxcd-r rf his 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 momentum, discuss r bd3vf9ot --ida.q:l why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propellerd :ar-l 3bi-tqfv d.9o can operate to keep the helicopter stable.

  Express the following angle* 3m4u:xv x9 p,devw3c8qevzes 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 coincidence. Calculate, using tl -i0vp5q; ksshe information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as se-k lvsqp5;s0 ien on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at tgw11 8 qaquc8* l a5+6(xpfvkxf 9wrmhhe Moon, 380,000 km from Earth. The beam diverges at x1m918+wagr(falhu fkcwq6 px*q 85van 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 th2duclfhbq cza9xbvg8()n0+ 1 e motor is turned off during operation, the blades slow to rest in 3.0 s. What9czux 0q1v nhb28cal bd +)f(g is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a3s;r(b /*i, 1w 30pat bpoexmyc(yvf o level floor 3.5 m to another child. If the ball makes 15.0 revolutions, wha(3bwf0;y aspyoovt1i3m,e*cp /b r (xt is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolukllf0qu2 e*9ws52f q utions do the wheels make? q5 9lq e0uls2k*2wuff   $rev$

  (a) A grinding wheel 0.35 m inqs7o lbl6 b5p 6-ptlybs457bs diameter rotates at 2500 rpm. Calculate its angular velocity i t4yb-5l7bqpop ss6l7 l 5b6sbn $rad/s$ $\omega$ =    $rad/sec$
(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 4.0 s (Fig.8*plw5cnwr 9 z 8–38). (a) What is the linear speed of a child seated 1.2wzcwr*89 5np l 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 velocitwvz h7f1sxdw0 i.u47v y of the Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of byp/av*s-,jga point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 bbsug,w.oerv;51l2ccoq 4i 1tg tm 35w: q:arcm from the axis of rotation is to experience an ai5ov 1bu w 2om:a1gqe t.sq,tl4b; g r:5crc3wcceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly aboutl4 cx 0jr rsr7zy:*mp8 its center from 130 rpm to 280 rpm in 4.0 s. Determir sz 7:x 48yclm*jrp0rne
(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 radiuzcq4s4 vg:um(rqy; c ,s $R_1$ 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 ab ut.fh4n( sak:oard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the 4.thuk naf :(sstart of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformlvd8nvmz/+i b4 y from rest to 15,000 rpm in 220 s. Through how many revolutions did it turn in this i+4 n8vdb/vmztime?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 r.xc y8wqz5d+ mpm 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 fl0p7 ry q9pgg+eying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reachirgy+p q9p0g7eng its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 rlbd)1 od0 q rzfl 8fxaqyp-;0.pm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in t0y ql bl8.) ox;-ff0z 1qadprdhis time?    m

  A cooling fan is turned ox 64g. /6 ;tai34dwechpkjx1s1vtxqmh j qf)9 ff when it is running at 850rev/min It turns 1500 revolutions before it ctcwx 44mk.9j pqts f1hi6;6j dahx q gxv)e1/3omes 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 tjwa+8- nw zu2speed uniformly from 95km/h to 45km/h The tires have a diameter8wzuna-+j tw 2 of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 r*ab3s:5ap4,(hsqpad mox(iu w bc 3m,evolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter *mwa:4h x(p,cm, qbuo d 5sia(3p3basof 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 cljc 85q6e7n koz53t5yl/jb vzz imbing a hill. The pedals rotate in a circle of radiubz6jk53jy5qz7t /l 85oezcvns 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 widet 9 e5ytlr.4gx. What is the magnitude of the torque if tt e4x gt9rl5.yhe 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 abouth7x y.h 8lj6y0fajpz3 0r*p3 ua0 hgao the axle of the wheel shown in Fig. 8–39. Assume that a friction torque of 0.43pp*yj60 rzy0g f3o aaxuahh 0h 8.7lj $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a massless zy*y3ag:;l(2 n/bvn ii2huxb0mpvu39 7 eqonrod which pivots as shown in Fig. 8–40. Init2y7xbqzp 0 ( v *m2o9l/ein3vguni ;3byhna :uially 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 require tightening to a torque d vo9ae8/e;-//i+djq fm jtfq of 38e/f q/eji /j-vqa8dm+ 9o;fdt $m \cdot N$ 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 rxh,jkxj3+6 c ofylc ,)adius 0.648 m when the axis of ro) +j lx,jk6fcchyxo, 3tation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter.a;c,lo+rsmjh;p3xh n u1.+kag*9md w The rim and tire have a combined mass of 1.25 kg. The mass of the huahn*3 aclrj9xh , +; m;g+kw.psdu1o mb can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rodxnhgs:t m b 851v--tzw is rotated in a horizontal circle of radius 1.2 :1swzmnxt8gh b v- -t5m. 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 potte+p)e9dmcr qh44)vcuvx m ( m;er’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and the clay is 1.5 N p; ev)v c(r)c4h 4d+x9mumqem 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 q*n(lb2 im 0mbarray of point objects shown in Fig. 8–43 aboulb mq* 2mbin0(t
(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 mah wna/p7cf7e6ul4 eqakm,*mh e* (4ilss is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite splg,,/q/2/yfk dd a.l zbs6ea jinning 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 steady force of each rocket if the satellite is to reach 32 rpm in 5.0 minse fdg al j/62a.ydb,/qk/zl, ? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with c 72 (y6b+*so avewziua radius of 8.50 cm and a mass of 0.580 kg. bvzi67so2a+c(* uewy Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a c-qj t)(dedw5g4 3j eo(x2oh bf7o2embat, 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 ev ) ahtv ,pe05qzk 9(skr:-ahhand-driven merry-go-round and is able to accelerate it from rest to a frequency of-s 0e5a,vte(pvk9qhr) :ahzk 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is eventually 1;yf d(97 0biinkra)puw wm c3brought uniformly to rest by a daf (y7k0i9u ) c;pw wimr1b3nfrictional 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 vs 0ukj. m.5 wbzu/c.9t7l7ubehnc)daccelerates 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 tr1w2e/vz6ney n3m ./kuf ls2rhe action of the forearm, which rotates about the elbow joint under the action of the tr 6nyv er lm2sz.e3unrf2k/1/wiceps 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 5ap2 zbcts 28so:tt*olong thin rod, as shown in Fig. 8–46s p8t* s:za2o2co5ttb.
(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 consistc 0et kr yd5bl;.9sv9ts of two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest within four full turn1 ap(edo,z6 rp 0zsj2ypf fnxqk6 b: 2*b7b)krs (revolutions) and releas) s 1r7,:xrkjbpzb *na06efkpqbz fyd62(op2es it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of inertia f+8k:,ip;cb8uv7 ;fuimtzydof $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develop ,,gxqgk um0n2c7hc5 os 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 down a lx.u tzy- 3o()in9ne zrm y84rmane at 3.34yi(.-xn9yom r )enzrut38zm $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of thg+rkyt1u 0td5 ltn.3/kv6aqae Earth with respect to the Sun as the sum of two .tkktg +a1n v utd/a3 yql605rterms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.50 m. H.z onl8h: k b+syb.ia;h. )8v zwm5yd(irsg1now much net work is requireg hd.iv81sb +yla5ib8nh ;sz..wro)(m:z kny d to accelerate 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 syx 5l+ 93z5rne 1cvcocm and mass 1.80 kg starts from rest and rolls without slipping doz3r+15x n c5y9slceo vwn 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 isg+5)f l9rbl b b :/*lzntlrq6t/lj1 pi balanced vertically on its tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground?lltbqn956jpt frigl:1l /r/zb )b*l + [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball roo0 pfny8rys03tating on the end of a thin string in yfn 8sy0pr03oa circle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momen u1u*f93tvtt) 5l at9z.zpvvntum of a 2.8-kg uniform cylindrical grinding wheel of radfvtu 9nz.u1av tzv t5pl) 9t*3ius 18 cm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at hitc* s x))le kawpz*8+is side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotatzl8 i+x**c)e) kws atpion 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 redfar/fs /* t,efuce her moment of inertia by a factor of f /f,afe/s*t rabout 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 increasewk7-* nk2 pcao her spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a final rate o a k72nocwp-k*f 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axis through its center fbrw7uq74suy 2k6uc3 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 rotating wheel. What is the frequency of the wheel afte u246u3rywusk7cfq7b r the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinnhyb2z)exxh5 4 7su+xi ing 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 cdoi-v*c4/1a g cwf;oi5s - hfmomentum of the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inertia I is dropul .n04)l vz (upe-j9hy dhcr7ped onto an identical disk ro) up0l z7uhdlchy e(9n.r4j v-tating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turnsdw8d ,n8q tv:hf72w 0fipy3yo at 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 merryo10mob byr)z l5 58kid-go-round platform of radius 3.0 m and moment of inertia 1obdr8kmz5yl o)0 5ib 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 rotating freely with an angular veloc*n zbyw)/ghaqm3bl2f,7;m5 ucli /dnity of 0il/abn2 yhun,b/dmw7 zmlg3*q5; )fc.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 aboutz(j9borcl s, te j255t half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum,zt5sl( er9btj 52,cjo 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 involdz:8 od t7mz:uve 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 0s;fonn:l6z22a cwg e$ 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 p4yii-ny 5 br3f (tdfo:;2pk s4o quh7entjb;8latform, initially at rest, that can rotate freely without friction. The moment of inertiye;un7 (48fb-o3ihrtk2no:yqp;s f 4b i5 dj ta 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 standv oo8r(ja :e ce-s6rd4s at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearin8eca6e4ors -jv rd:(ogs 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. y-b9yj ge)he end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s cenj eeh-)y .byg9ter of mass move?

  The Moon orbits the Earth such that the same: sb3(t.djpga s7ol/;.z a6qfyrv3j u side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) tog3jbs yf ;z :qlv(6/3jd7ra.s. p tauo its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates fr*b c 1 cot/,e.4nzjci he+6unuom 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 0s3ax +iyz/eb uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque dz+esb 3i /ayx0elivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two owl8o6sp-a: o solid cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin sa :oswoplo 86-olid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular sf+zst.ow 0 eblsa0ddfk4:+v*h8 o: zxpeed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but wit)hwf b o2oedt.3s;z* +)f5z-af emvcg4l8ovfh mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a unifo eo; 2 fw5)o* so cfmz ffhegd)-8vblat.3+4vzrm 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 e-zs,4-s8mh*odm zx 9rmlq .jsnergy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 9rlxs- .dm8q4j*s- z osm z,hmkm 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 k;5 x+kyd x7xcrohqjm 3eajh*, . 1qr+an $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizontalvuqo -dlte9o *na4t/ z) xq 2k2bm)m4p 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 fri5 4riii(f-hfw.lzgup :j7 zb4ction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally flz gf-i4z.: pjiu iw5rh4(7band 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 verua8 iw;inm b9ju3b l4,swk,z )kc ,+arh3ixd:tically on the floor, and we want to exert a horizontal force F at its axle so that it will clim ),s k9ala,i8x iu+w3bzi mk3n:u,jcwr4h ; dbb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road iszw ze5 8f+b.9et.,rougpr8 n q making a turn with a radius The forces acting on the cycli9p.ez w.nrf z,+eqtr8bgou58st and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling of length 1.5 m and begvcb/q5n*m yj+1u qg pcxp)a8 2ins whirling the rock in a nearly horizontal circle above his head, accelerating p+ j bc*1xac8gqy/m5)2unqvp it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thin rodshnhb9w3 ;w-ca, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly againsc;a w9b hn-h3wt her body.   

  You are designing a clutch assembly which consists of two cylindrical plates, oxzofgmovn*c m9ol f9b5r 0y5n(u k,4a+ 83lpxf ma rf*z5v3(xx 5g9ll9ocok pnn 8fay+o mb,mu04ss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 k i9jix 1 .fw2t+ena)btrack of Fig. 8–58. What is j9 .+n2atfkxibiw )e1the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not ass2u)jcd zq.7bm ume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolut i/u7kfr1cu-aions as the car reduces its speed uniformly from 90km/h to 60kau7c-1/r f iukm/h The tires have 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