A bicycle odometer (which measures diso7kw2sd6 7d fevdax 4o(3(hoptance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with2 vo(fkodx6(d 74as d7w eo3ph 24-inch wheels?

Suppose a disk rotates at constant angular velocitw+. 7/2ltmfuud5n*0auk wu ,vpiw h v,y. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the ,wnkl, avmdtu/ w.f uhu7*+iv520puw 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 valgft*fpkw6h )vhf3 --c ue of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a largn3dhja478( d0mawpd c er 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 your hands behind your h2gccf5n2 n3eg8xj xrvb /a:g6ead than when your arms are stretched out in frgnxrjf: /58 g6b 3n2ecx gavc2ont of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at them4f/a1vqsgr*r8dz a ng(y1l 4 rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front m vg1ry4z4( 1r/la*a fsn qdg8sprocket or a large front sprocket? Why?

Mammals that depend on beorr7nic )atm*/ok6 edv. +cc 8ing able to run fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On th6o keman oc t.)i 7ccdr8r*+v/e basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow beam?1pgo ab8 jf0mfs8u* s.

If the net force on a system is zero, is the net torque aib,s/: vtl yb)3yyq f6lso zero? If the net torque on a system is zersyby/ ) :i,tfqblv y36o, is the net force zero?

Two inclines have the same height but make different angles with the horizo27 h+ oepazz -92zifdjntal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Expohfp+2a2z-d 7j zzei 9lain.

Two solid spheres simultaneously sta-0fqpvv7amsf 2ss4; u rt rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the oths 0pvmvsa-s4f72u q; fer. 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 radiusmgvw(2we z 9c (p)v4wq eol56c and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which4v(pgvm c(zl9w) eo c5wew 6q2 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. 2;mtt41vlm3ndl i5h wYet most moving or rotatin;wmli2 1nt htvd3 m5l4g objects eventually slow down and stop. Explain.

If there were a great migration of people toward the t*t y8jobbpud8,s5 w0 Earth’s equator, how would this affect the length of ttp8,uy s5b j8o0b w*tdhe day?

Can the diver of Figml9ob8t chr+tpelbd0);; cg- . 8–29 do a somersault without having any initial rotation when she leave -bo;lh)9;8 bgmdtr tcep0+cl s the board?

The moment of inertia of a rotating solid diskv t93,.z6eba3q zbkrvz *dwan u*n 4xg,ap//w about an axis through its center of mass is p6 xb* w4.,ba 9g zk*,/vuta3v/qn eandw3zz r$\frac{1}{2}WR^2$ (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 l6(b -rx gyy xlygbwm+s 1+, -,vcj0ymon a rotating stool holding a 2-kg mass in each outstretched hanm-lbyx0j- m(v6y+b,sy xg,yg l rc1w+ d. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and w-7oi td5)6*x vp b40mkn itmjhave the same mass. However, one is hollow and the oth*t4bp7iw 6mi0m)kotvd-5 njx er is solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle points west. In wmha 6+u/hl yj,hat direction is the 6hj umlhy a+,/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 standing on the edge of a ld5yz,;e9 mg ydir)r l/arge freely rotating turntable. What happens if you wa5d g /9y) yr,dm;zlirelk toward the center?

A shortstop may leap into the air to catch a ball and throw it quick0d, ugf98pdv+z *dd hvly. As he throws *0zdv +puddv ,h89gfdthe ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of a0m w7tf4rweli18pg vrtg ,o1 3ngular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the hel,r 4eg8ti7r pg0m ol1tfvw3w1icopter stable.

  Express the following angles g la7ty*:kbfh rxtuj l-js(1/31wfw2 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, usex-dx qp j-r58j,xve- ing the information inside the Front Cover, the angular diameters (in radians) of the Suvxpr qj x--ed,e-x5j 8n and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. Thhvgojnx ;s0k c0; sn8;e beam diverges at an kcsgn 8x;h;oj ;n0s 0vangle $\theta$ (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 650 gvi01r*qt u oib6h.)j0 rpm. When the motor is turned off during operation, the blades slow to res0o* v6q1 bi rg.tuji)ht in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on as5fdd-m 9915lk vobkn level floor 3.5 m to another child. If the ball makes 15.0 5 v-91bdlfdo5nmk9ks revolutions, what is its diameter?    m

  A bicycle with tires i12;yrwcf tq6 : ;zjl-*gpgl q68 cm in diameter travels 8.0 km. How many revolutions do the wh ri-gw6qq*1cl ; gyz;f2l:j pteels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. C6quqbhe57 kuz1e z 7caa4df5+alculate its angular velocity in6kh f7dq5+q745 aczuze e1 abu $rad/s$ $\omega$ =    $rad/sec$
(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 ml4h g;q) 1sdnp7z3j trwva./complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child sea1w3l4/7zn.a;d v jqsphtr)mgted 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) injy* kez)5z+igv ; rc,nuv5;kx its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a poibu ovq l;uf/*jw/p);z nt
(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 pafb nwl 2mcj+y;byx31+rticle 7.0 cm from the axis of rotationbcl;n w3 1+ yymjxbf+2 is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates un te 2 ;upg85ow3.saxf,8ps9 ddckqud-iformly about its center from 130 rpm to 280 rpm in 4.0 8;,s. spou3 dt equ kw -agc928pxd5dfs. 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 radius echsgog(a1+ pxqsxhv/ wsn+9/0i,* u $R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$

  In traveling to the Moon, astronauts aboard the Apollo spacecraft put themselb xvcdp 092y546jjuokves 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 interval. The spaj56vy 2c kjod094bxp ucecraft 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 us-2o.q m8j5ii0q nvomniformly from rest to 15,000 rpm in 220 s. Through how many revolutions did it turnm jq.0i n5m8osivo2- q in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Calculak,( x/bngc h 5ve73ubste
(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 pjc*tm yur7wc.v0j0 0a whirling “human centrifuge,” which takes 1.0 min to turn through c 7vpymuj*0.jr00 ct w20 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 u(z m-ana-41i0rmw5agg9 fa awniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in this tima-i9a0z5aw m(r1ng a4 mw-afge?    m

  A cooling fan is turned off when;yh,1i dcu ;nh it is running at 850rev/min It turns 1500 revolutions beforeih1nc,d y; hu; 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 itmbzfl3; wn-b j -m.eq hz(b)4bs speed uniformly from 95km/h to-n-) bbfm3qz.(hbe;bl mz4 wj 45km/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

  The tires of a car make 65 revolu4ibgic z,o a..tions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.80 zg. io.,bi4c am.
(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 alvawj:pzpn*+t; d c+rm: 32ikr l her weight on each pedal when climbing a hill. The pedalt pvp:;dw 3acj n kzm+*r2+:irs rotate 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 Ne4(gf8t1zm ekr5bavu )h.b)me sd:h , on the end of a door 74 cm wide. What is the magnitude of the torque r) ueh):b,fa4ekt5(1d8m ebmhz .gvs if the 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 of the wheel shown in Fzq1 bfq8-t . jx3t.b8vm l1ytzig. 8–39. Assume that a friction t1.zvyf18xmbz-tb 8 l tqqt.j 3orque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, a(dot* m +eb goo (ko6l:n,l/tbre attached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the ( l:bltoote,o d *(n b+6ko/gmmagnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening to a tn7bmo: xr .l:torque of 38t:.lm bn rxo7: $m \cdot N$ 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 radiuc/587nqh y uais 0.648 m when the axis of rotation is throc a5yiu 8hnq7/ugh its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicyclesi ujb-- 4nrm7xcb 6yd35;r rj/yd9lm wheel 66.7 cm in diameter. The rim and tire have a combined masm 7dr6 d/ -- ;rrxjl3isy 9ymb5n4ubcjs 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/lk wsf dfw74 5+sd6a0vywex; t yb-x4 of a thin, light rod is rotated in a horizontal ed 5-da4/;v4yxbfw06twl yf+x k7w ss 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 b0uzlc emi 5/yi6mz06angular speed (Fig. 8–42)6/5m0mizic 0ly zb6e u. The 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 8 oswa8-o*enq4usu7d45 oss mn 9vt 3au.qc+yof inertia of the array of point objects shown in Fig. 8–43 aqnvst uc *e5s 49 .sooa om48snuuy+7a8 d-q3wbout
(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 two63jdsz6* jyd8t h. ymc oxygen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning at the 1/rjms ;6apox l-.il galp*;zcorrect rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the g.l/ 1jlzmao a;s-ix;pprl6*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 uniform cylinder with a radius of 8.50 cm and a 9ha(a tse1/o5vvkx a, mass of 0.580 5/e ao1 has9tv(,k xvakg. 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 bat, accelsj +:.gtd g*7yb:i g tiq/neg;erating 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 merry-go-round ml +gj wc5;4)v jgztt-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 om-gjt 5wc+)g; jv4ztln 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 eventual q(m+ r fj7hayjdk-8y5ly brought uniformly to rest by a friction 8yq- yjrm+ jhd75kf(aal 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 acceler .xj u9foeg2+d2h n:8 ;uzphpnates 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 solem/+xiz3a9)9it lu cu oly by the action of the forearm, which rotates about the elbow)omazx+/3iuucl9 ti 9 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 rovq yfx9pi6 g8t q.i1-yd, as shown in Fig. 8–46 8iixty96yq.1 -qpvf g.
(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 cons/;h-p))ejb+l4l6b8sa mvly(u n2 payqlku.xists 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 tur;vjkddsz37;gs z j(r03 6 fauhns (revolutions) and releases;(j dzs3 su6ra73;v 0f hzkgdj 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 ojxo:d0 2zm6ma moment 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 develoka *chiw);-rn ps 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 radiusvktk ipnb deh:b9;6021 vc. gs 9.0 cm rolls without slipping down a lane at 3. vi 1hesbtdp09. 2c6bn;g kv:k3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic ene0 b i3xo.i;yeuq dc,s-rgy of the Earth with respect to the Sun as the sum of two ie ys;uc i-x0q .b,do3terms,
(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 6j,hq8bh-kicmass of 1640 kg and a radius of 7.50 m. How much net work is required to accelerateh ik ,8q6-jchb it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.8g (/apaa-k+qun5se9ne z5 6m;3.efyuo p1lcd 0 kg starts from rest and rolls without slippiq /+95em.y po pgnlen adkuf-u6 (1as3e c;z5ang 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 g5p9rcel ) uwe)a 05nyfn52nn 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 thegyne 2c55f9w )n 0urplne5a)n ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.28b3gbk 1s .il7 mj*via10-kg ball rotating on the end of a thin string in a circle l*sgb j vkbii m18.37aof 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 cyli wx7)n meo(v11orzby74r to 8ohe;lz+ ndrical grinding wheel of radius 18 co heomo x7re;l7(bo)8r4zn1+1 tyzwvm 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 his side, on a platform that is jb4 mhf.qmwb;up.5( orotating at a rate of 1.3rev/s If he raises (bm.oh.45j qu ;w bmpfhis arms to a horizontal position, 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)m8v;e1ir ;q7n0xymhsw;n ge,5k v pl4 can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she maygp,miv;hqk rxn07v84; 1snw;ee ml 5kes 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 increc2vsfs4 e 6m3 )imsv,mase her spin rotation rate from an initial rate of 1.0 reve23fis4svs6vcm m), m every 2.0 s to a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axis the m1a 96nfbz( a-d wcmpc9ig/4rough its center at a frequency of 1.5rev/s The wheel can be consideredfbiac16pc9a9m4 me(/ -wngdz 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 after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spi)6l5 wdv8t*z(vhz j lcnning 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 ofz1 )ac si)qnl( 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 dropped onto an xwr1ps ck-y5ab xb x u/f9j,95identical disk rotatik /5b99 pca,y5fxux s-1wrxbjng at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4 zmm5hk.usm7,:kg : ot $rev/s$ 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 sta9 b**nbl w7jfo2 *unxonds at the center of a rotating merry-go-round platform of radius 3.0 m and moment of ine bu2ojxfb9 n*7nlw**o rtia 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 f wtw0*psww2 d,,9w urwreely with an angular velocity of 0.8,*d 0swu2p9w wtr w,ww $rad/s$ 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 evens(sntd88etu 9pf89d 7p yr4 nv f:ikb9tually collapses into a white dwarf, losing about half its mass in the process, and winding up with a7t 9i 9u4 (9sfkntef ddr88bynps8p: v 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 involvprv)xb 9f/f z-e 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 vh r,m2 qa xix cm4wx5z(o-:47fg,b zd$ 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 a8ar ,qbs9xo7bki 9i*rotate freely without friction. The moment of inertia of the person plus the platform isi x7ob*,sk br8iq 9a9a $I_P$ 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(-k fcr0+ y gymcuyhdz88*q8x turntable that is mounted on frictionless bearings and has a moment of inertyz-ugkd+0c8 cr ( yq*m88h fxyia 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 ropexontsl ,bsxu(cq*08as (; qiipa1x0, rolls on the ground with the 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 rou 8sx,0*ba1l ci(t;qx qxn,ssi (0opalls 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 samey6u8b +nkjl+fhpo p6j+ul ;x5 8vb+ ei 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 the latter case, treb;ul++p+ e8y bij68 ojv5 hk+flpnux6at the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates r.ewfzv*v uk/q3 y)s5from 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 oowo *+upp-b y+f radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval pow+ +ob*u-pyat constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of bgg:4)bbr v+ypz2+ bbtwo solid cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 pb) +:+2 bzbgbvbgr 4ykg 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 angulxb/, ky/- sncc uc ro,f1r6)qaar speed 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 with mass 8.0 uxj5,zmz6v .xnc*;xe7r+ iii 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 vxu,5;m+i*x ezrj.ci xzni6 7 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-pollutionl.v de*k0(0kx* m/tlh so9fee automobile is for it to use energy stored in a heavyle m9ovkf*e e/dk x0(.hlst*0 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 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 illustrat8 a n1zev)a)vs6ip4pv es 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 horizontal surfaceowo7*n iyo1eh3z ulbo;k9r 3 * 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 frerkjz:mrq(g/. ). vku lely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass o /:jk. )r(uklrvz qmg.f the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on the floor, and w9 +zn s yo6q)9luoix lixy;.)re 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 y qz i)l+u)xyio.6n9xs9;olr h, where h

  A bicyclist traveling m8f*g g y9knp 0k4z6ciwith speed v=4.2m/s on a flat road is making a turn with a radius The forces acting zp 9fkn0gick 8ygm 6*4on the cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling of length 1.5 m ac;3,dmga04ehl hpn 0wnd 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 the torque required nl3eh0; h4a gp,d0wmcto achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylv3l sv9n-.i qainder and her arms as thin rods, 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 agvqn .s9iv-a3l ainst her body.   

  You are designing a clutch assembly which consists of two cylqq(gv w 4 :r3djai0d0lindrical plates, of j:3l w0(qi04dagrv dqmass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 ak+ci/j ( : k.v,ykajc:*s awbbnd radius r rolls along the looped rough track 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 h.kck+(i ka:byjcvw :/b j,*asighest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but d:;*86trd-1/wmzmx/lk uzf5aq ektc y8 vv , nno not assume $r\ll R$ h =    (R-r)

  The tires of a car maf6h ftxt-1 ;q lpzz).ys w1tv/ke 85 revolutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of each ttzf ;-v)lpty szx.1tq/hw6f 1ire? $\approx$    $rad/s^2$(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