A bicycle odometer (which measures distance traveled) is attached near thfkfck52q5+qmt e 7usx5(-lx we wheel hub and is designed for 27-inch 5 c- qu5k5k+ 2sxl7(qffwextmwheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant ab3g w l7nfb6*engular velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly*wb fe7g6n l3b, 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 descridby4xi w-05zw bed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force?,1lwfpru l;gh9x 5i1 y8dzv5n 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 head than why1f(y ua i9 fwz2/22mg7xxymcen your arms are stretched out in mgc7wy(2mf ax 21iuzy 9yx/2 ffront of you? A diagram may help you to answer this.

A 21-speed bicycle has seve0+dhywh33w w2r - jnspn sprockets at the 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 sprocket or a la3 2 -w3phdywn+hwr sj0rge front sprocket? Why?

Mammals that depend on bei8wv9 zwq-3cj y 4h7u2eprovh6 ng able to run fast have slender lower legs with flesh and muscle concen eyhp 3wrw2c u49jhov87z-q6 vtrated 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 a loce b nsrq7m6-*sw1fo l dg8e3;jz4s1ya/ :qsxng, narrow beam?

If the net force on a system is zero, is the net torquej81v l9ti1xd :fgqg o3 also zero? If the net torque ogq v8 dgl311jox:f9t in a system is zero, is the net force zero?

Two inclines have the same height but make different angles with thuceez ppw8 xebn j m*0ic111:3e horizontal. The same steel ball is rolled down each incline. On whiw bcz1xueim :8e3ecjn p11 p*0ch incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start xx/ dkrwduw9)+x3eo+ rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at thx3 rxwd 9xo)u ekdw++/e bottom?

A sphere and a cylinder have the same radius and the zf+ u3mx4 7v+fbjs3ew same mass. They start from rest at the top of an incline. Which reaches the bottom m+3fe zsf7xv+wbj34u 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. Yetkn06rg :hb9m h most moving or rotating objects evgn6hk:0h9 rbm entually slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equator, how would w98pe; eg5vhg this affecte8;9e 5p wgvgh the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any initial rotat)0fdv75ad qi4a pilmdah5*y ,d1 cbq+ion when she leaves the board?qpvqd )1 adidm7a5h, *+yif 5l0 bad4c

The moment of inertia of a rotsx/7axz7q0rb ating solid disk about an axis through its center osrq7a7 b0xx/z f 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 smi +,e-a i2bgholding a 2-kg mass in each outstretched hae,ia mg s-i+2bnd. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is hollow and t vmp5yu 7g8u5j4u0 ffjhe other is solid. Describe anuf7mj juu845 pvg05fy experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal ajq g5jlig c7zf1c:;w, xle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points eajczl j7 ,5wc1fi;g gq:st, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotae9.dat 2-+ okhy:qq uhting turntable. What happens if you walk towarded qhuy:+t9-oha2.q k the center?

A shortstop may leap into theo,kw;hb9samw:ijf0d is 0g/8 air to catch a ball and throw it quickly. As he throi9b:0wi8hwj ;ks,mo s0d g/ faws the 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 angular6 sgl8f lsrc4l-xzu m/lbv:32 momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate u8sl-x46v2mz l fs3g/blrc:l to keep the helicopter stable.

  Express the following angles in n l gq/tu/sor1 9 gvmjd-q- -a,gp4p9kradians: (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 a5 x)fzr- 8lb:dfk9kusmazing coincidence. Calculate, using the information 8 zd:fk-l9 )rsbxf5ku inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam uumx6y h89x0 rdiverges at an 9x0u8mr xu6y hangle $\theta$ (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 motorxja* kmeerz7). eyvgk1i0p *yih50u8 is turned off during op*kx.h8y i70eez51prv0u ) g iy*aj ekmeration, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a . ;c(sjrgvjl:level floor 3.5 m to another child. If the ball makes 1 (:jsvlg; r.cj5.0 revolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameteeb)td.t3w y lxsg.)l)jjg:3d r travels 8.0 km. How many revolutions do the w l lb3jdsw.yt.edg ))xg):jt3heels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates c35iumotrwt8ekd5 9mjkb9f -:nv:) m at 2500 rpm. Calculate its angular velocity in-t59i rmunwd okc8j e:k:t)m93vfm 5b $rad/s$ $\omega$ =    $rad/sec$
(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-roun g+yn9+q-nnhw 3jtv2bd makes one complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear spg+-qt+n 2hn vnbw3yj9eed of a child seated 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 Eap :we c*cqz5h*;)ddd e*q:xgqrth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear sr( ls9pmpini/d2),gjpeed of a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if wxv/s(*ysuqwy y *fr 6:ep/ (xa particle 7.0 cm from the axis of rotation is to experience an acceleration of 1s/* r(qx*xyu:/ws yp6veyfw(00,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpm tc: pi;htma7 ;yer +go7i*/ pifo 280 f*;p7+a yc;io rt :mphiie/7grpm in 4.0 s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radius 5k-div6s5/ ,wdi ;v oylek3yc-x7qk y$R_1$ 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 themselvesr4yi.4i, wbco into a slow rotation to distribute the Sun’s energy evenly. At the start of tbyc4 i ,irwo4.heir 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 uniformly from rest to 15,000 rpm in 220 s. Th/v5egqm g xx57rough how many r / e5xq5gv7gmxevolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm bat/rj0u*- us sxp, /bto 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for (q7iv*)e wola the stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through ol )iev(wq7a* 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 acce- ghzphjzr0mz oea 6/3l0z w6:lerates uniformly from 240 rpm to 360 rpm in 6.5 s. How f6pah z: m60wj /h-gzez3lroz0ar will a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when i .+z v:js7mxcin3 del9:6ojbsey )n;mt is running at 850rev/min It turns 1500 revolzjjelm3 d nm9x.n6: )vy;oce+7:sib s utions before 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 reduceqjb7 lu8 i66gtijzw49s its speed uniformly from 95km/h to 45km/h The tires havj4it6jgi9q zw 6 l7ub8e 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 maker(cs01s4+t te/lbh * b,rr ig60ons fn 65 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a dibnrer(bofst/041r* 6 ,snig0tch ls +ameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on each ped5 dt9bq.4y*qz4nvgjy al when climbing a hilltyjgvqdn4y. z 49b5* q. The pedals 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 N on th8(ozazy 97xkzr;jh8 pe end of a door 74 cm wide. What is the magnitude of the zayr8ojzk;z h (8 7xp9torque 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 Fig. 8–39. Assumej2sk(ijaj1 nn :jq103db0e fd that a frictiondj0 jjj(dn0n kbeq1af3 :s 1i2 torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a massless rod whiytq.83o ik0iz -.j*(ho uoe kxch pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction o83ok.thx.k0ze*uoojqi (-yif the net torque on this system.

  The bolts on the cylinder h7 p ,-lpael1bbead of an engine require tightening to a torque of 38l7,elppa- 1bb $m \cdot N$ 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 radiu5o,qa wfd8: bds 0.648 m when the axis of rotation is through its cbd,oqw f8d:5aenter.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheelhohitej0o0dm- k+2n; 6rk)ihf 2yt 9y 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass ofrfh 6tj-it+o; 9id y 0yo20henm)hk2k the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotate2vggr3pd j/mdpag 3-(d in a horizontal circle of raa23/(gp - jr3pm ddggvdius 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’, ;f.hiu j-akis wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and k;ui j-f.ahi, 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 of the array of point okd63di)fy3 *1t bgkq1 ty gnb6bjects shown in Fig. 8–43bgb* 1dn13 y)it6fq kk gtyd36 about
(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 ug,sq+b . vlu6ejw/+r 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 cyl1fw *y7qi0rtg+vd,ww indrical satellite spinning at the correct rate, engineers firerw 0wywvf7tgd1+iq* , 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 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm and a mass o(j;296oh/nnl cefm w of 0.580 kg. Ca6wm;2nolj /9( hnfcoelculate
(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 from rest tq jojabn+q* cs5+n: 8so 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-dri5zm *y (*9cu ll(iiomcven merry-go-round and is able to i(( im*9z ull*ccmyo 5accelerate 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 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 10,300hqh2msy h, ha q.md/r 131i,et rpm is shut off and is eventually brought uniformly to rest by a frictional 1q,ryhh meh12qi hs/a,d3.mt torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a 3.6-kg ball 74n c2; anniao7 -.c+pvr wwgwat 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action of the foxyqom1:e7(e h1 jc /e-uu*jb gucec/( rearm, which roej/1e- 1c x h:gu(uem bo(ujcy7e /*cqtates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be conf/ qj9iqi*tvp-) zc7 qsidered a long thin rod, as shown in Fig. 8–49qf/zv7j itqp i*c)-q6.
(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 con2j(a cd gm51amh)swp,sists 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 acceleratesa8cdiy6 g3t9y the hammer from rest within four full turns (revolutions) and6 yy3a89icd gt 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 moment of b4ejm f.myn:.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 develops a torque of -2x8arohn*hvr mfb ;j1s49c rgh vr+.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 s zg-wjv( 6sjr1lipping down a lane at j1vgw6s j(rz-3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth wi s-: maae4jntey-u,6n6so xldk48z 8ath respect to the Sun as the sum of t6o- eael8xazn,ym d4:6anj- 8u 4tsk swo 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 ybzp ,v624 uwaw1lxzahmt31( 1wm.hbkg and a radius of 7.50 m. How much net work is required to accelerate it from restb6 yu2va1m.w z31xh,(w bz mlhtwp4a1 to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts f0a5uhdy5o*/ ,rkq khwrom rest and rolls without slipping down a 30. d q5w0,hh/kuko*5ry a0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is balanced vertically on its tip. It starts to fall and i55;wif n0fjh(1yjewr ts lower end does not slip. What will be the speed of the upper end of the pole justywj50fn;h5(1e rij wf before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball nran(x tw+n;8wk2 .q1nve p+t rotating on the end of a thin string in a circle of radius 1.10 m at an angular speedn 1nk+2+( newp;rtw taqvnx .8 of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grinding wheel f8c:7 dzk bphx+ugzeoo,lt*km(3oz,o1 + by )of radius 18 cm when rotating at 1500k o1go:uz8ob yz 3b x)*d, lph,zme+t+cfo7 (k 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 +8e i9jdz i/ v7t8/)ndbnyaf3 oca/p fplatform 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 rotation decrdi/ 8v / d79bp8fn)3i zcajt/o+anfy eeases 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 momj,m*mf p8 .6 a5h:wvgjww4gp ds4 l+fz/b7xlnent of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed 4h:wml6w. 5 f*8v4bjwx7+md/,lsg pp fznj ag($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial rate of dp; rlw- 426a4ugctedtof,1y1.0 revowr16lf;dtt uec4 42, gdya-p 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 through its center at a fre uzlr 73m wii-03uum/4;qdkih quency 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 th3k 4ur-mludq 3 i7/w0 zmiiu;he 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 spinning at 2ull7hy3b;+do ql(di 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 mo9b:g(/qztcr0x.l9qj0 6zzl nr c:jlw mentum 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 dropped onto an identico8ew zxv 9mm9 xl40pj1jv0-seal disk rotating at angular speedexop1swvj jz0le m0v894m9-x $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns ab d5 60wpj3g 57ndwkfct 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 centea/l33zb,wy j y5lf ub*r of a rotating merry-go-round platform of radius 3.0 m and moment ofyl ,w3l 3zbfu5ybja */ inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is* plo*db2 ipw7c+c)l i rotating freely with an angular velocity of 0.8c*cw2o+*llp7idbi p) $rad/s$ 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;riw 0;vxxtuz xd3fv/) cdq;7, losing about 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, what would the Sun’s new 7 vxu)qdvir3x ; x0fwd/;c zt;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 involve6 w9wsla i.zyta9:ggb8v -m2i 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 ,3a :ulf yoh,m$ 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,s+9)j l u2dzmk initially at rest, that can rotate freely without friction. The moment of inertia of the person plus the platforlkszu +m2)d9j m is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m diameter m*df 3i8lwkrq- erry-go-round turntabllr8 d-iqwf3*k e 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 of the rope lgxsm i ww1;v,:ying on the top edge of the spool. A person grabs the end of x,mvgw:1; siwthe rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always faces the Earth. De0 e5skr.l2 fcstermine the ratio of the Moon’s spin a .02 lsfe5kscrngular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of 1 c2f 5k7 wj ,usgqrb+fh)qbs99m/$s^2$ 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 :gnv3 (aixkhlw- u4 :zshape 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. Calcuxn:3z4 uv-k h:agl(iwlate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two sol7*a dienc(hhdz xp0:4om2xb 5id 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 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it0i xcah hxz( o2bn:*de m75pd4 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, ho:kju w*a 5va13kzwl w/w is the angular 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 ib2h,l j :*sg9bpxym3times 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? Asslhi mb ypgj3,29 s:xb*ume 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-pollut8n9z c/m0o6+ :rh/qwvxtojkqjg b c2 6ion automobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 140 : cnvhbo 6 2jo9rjzqk8qgt60cm/ /wx+0 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 illustrategsuvg fu5 /-7ns 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 horizont507ws ion8wl mal 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 mas0*eak bkpn 19anc o,zo(-z3us fcj ,*as M and length L can pivot freely (i.e., we ignore friction)n1pcz0 j snca ofa3 ,,**u9b-zeo( akk 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 of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R.*r0 zom/ ba7ma,eer/j It is standing vertically on the floor, and we want to exert a horizontal/b oa/jmrza e*er, m70 force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling wi4 lo,e)aut. o(teu u2dth speed v=4.2m/s on a flat road is making a turn with a radius The forces acting on the cyclist and cycl)uleut4. (oe,od tu2a e 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 rocg.j)97 nmxu1ixksq/i( vd qqf.e6p- lk 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 )xq-kmigqvp (d/un7 61 9..jxlfesqi 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 cylt:ns wg 79p23a:h rbuvinder 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 outstre2tnhgb:ua9 7wsrv: 3p tched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which co9qy5 2k g zjzn21pje/dnsists of two cylindrical plates, of k12d /9gqyej5 zjz2pnmass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 trwp-xk*+.0bgmk7o q kv jbd (i(av cd;,ack 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(7bc; g0qvbkv a+x( dm ,jiwk-d.ok p*e loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assumen6ka wyiy3 * omq4m(6+z *jokh*zt +im $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as zbmp-rvus6m y w3a*/.the car reduces its speed uniformly from 90km/h to 60km/h *wz3ya m/p-mv. ru6sbThe 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