A bicycle odometer (which measures distance traveled) is attached(nd grzt*ux 84 near the wheel hub and is designed for 27-inch wheels. What hatxnur84 ( zg*dppens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular vel i2d s)nt/n1w :nq e2qutuv)g;ocity. Does a point on the rim have radiqn/qn )tuw gn1sdi;te:22vu)al and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body w s4-e+vg w:udbe described by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a l5w;jsww+moo+l . 1vx si)6dbvarger 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 hsa+ l*is0w)dsead than when your arms are stre*)ss0 la+ wdsitched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the;*4y2q6gnw somc wcr3 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 smalcq;yo 6m*wc 4g23 rwsnl front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slendea,.a 6tx6ylz/ 3v(f o2e bxudbr lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, ebdvbay2e/3x6o . zl6t ,x(afuxplain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. lozx2n/(vc8a 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If the no+1oqe( y +bx9b hx8iaet torque on a h8 b x oqxoi+yab9(1+esystem is zero, is the net force zero?

Two inclines have the same height but make different angles with the horitdgrf6l(j6 5bfg;d)bzontal. The same steel ball is rolled down each incline. On which b6jgb6d f) gd(ftrl; 5incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres sime y1p*m0 mowi/ultaneously start rolling (from rest) down an incline. One sphere has twice the radii/m pyw0me1o *us 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 s lv9hs(tmq;xg3 t7c8mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greslt;tq 3 xsm 9vh7(gc8ater rotational KE?

We claim that momentum and angu)r3 db*cc9nofs4b /,kr *rcjilar momentum are conserved. Yet most moving or rotating objects eventually slow down and sto,) kscdfn*c/jr3o 9rb4 *crbi p. Explain.

If there were a great migration of people toward the Earth’s equator, how would fjzfflpr;:nk1hy1(v, 3bq1x this affect the lenl, kv yx1f1r3 1bp(h:f qn;zfjgth of the day?

Can the diver of Fig. 8–29 do qk,-rm) r ga(ja somersault without having any initial rotation when smra)q krjg- (,he leaves the board?

The moment of inertia of a rotating solid disk about an axisxihy9g/ --us6hp7 drv through its center of masspvy/u7is h9x -gd- r6h 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 holdingp6+o2 klm.xk y a 2-kg mass in each outstretched hand. I2 p o6xk.myl+kf you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look idents. rxy7e(x w.vm) hro/ical and have the same mass. However, one is hollow and the other is solid. Describe an exper .yxm/x osv e)wr.h(7riment to determine which is which.

The angular velocity of a wheel rotating dd ,xs9v6 r-tbon a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angultd r9xv bds,-6ar speed increasing or decreasing?

Suppose you are standing on the edge of a lar tbi)l/u8 1sq ;1iguqlhnn96gge freely rotating turntable. What happens if you walk tow;/6glq9i 1 h u18ibngqu ns)tlard the center?

A shortstop may leap irr5 qui- ,; wugx; q(pe-bo.hx83uthrnto the air to catch a ball and throw it quickly. As he thrqturhru3 p(8ew.ix-gbr5 ;ox - hq,u;ows 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 o7-ua;agkg6 y q)axrs zx7k37 of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or 36 7kxazuay gq;ox r7a-7s g)kmore ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radji lxzl4u:bin(, zl.9*oiy4 uians: (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. vpm jbr92/m p3Calculate, using the informationm/pm2p3r9vbj 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 divcl:2va 9n37eqe i 6sgxerges at a3ae i9s:ql6c2 vexn7 gn 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 ocb t/ 7-si;f.8jcbjx: cazx w*f 6500 rpm. When the motor is turned off during operation, the blades slc c;ifa 7cz* b/ swx:xbj.t-8jow 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 level floor 3.5 m to an(zw-;)upg f3kuna dn7 xex8dck2c v; 2other child. If the ball makes 15.0 revolutions, what is its d xd2 cakd;c;3gv(nzu2-fx78k)pw ne uiameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 1 ci(2isdbgl5km. How many revolutions do the wheels ig1id 2lb(cs5make?    $rev$

  (a) A grinding wheel 0.35 m in diame*)qo+ t +6 ch0smwmet;+d5zed 5bosw rter rotates at 2500 rpm. Calculate its angula +omd b+s)eo;s dt605tm*z5er w+wqhcr velocity in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complflh:3p/ ;ppthk5:b6 ,wb /bx -qqk xloete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a childhk bfx;ql/k :w 3qlppxo5btp- b/:,h6 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 Earth (a) in, nye/ b12mgjx its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a cd(t4;tn k1stfy7 d:kn f)nfi/l4nm9point
(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 cm from the axis 408l;h ;i7osc u si/hhm gw,buof rotation is to experience an acceleration of 1hih/4 gmu s l7i8obushw,c ;0;00,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerb)d* w75utsaoed9 ju3 kxfl)6 ates uniformly about its center from 130 rpm to 280 rlsobdtdua)xe7 )65 wku9 *3jfpm 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 f( q 4iyokoz(dl 75y;a$R_1$ 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, astronkt7zx gz ( r;h53 4:ahxv2pz xg-iadpi)p 2zi+auts aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s ene;z (2kgazxt a3gi5pi7zrp2z+v xxhd hi-):p4rgy 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 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. Throuna5o y6q0pmy;2j wr 0cgh how mar y0; cw0 n56jomqyap2ny revolutions did it turn in this time?    $rev$

  An automobile engine slows down fv woz0 nyq1kd--dv9foj *h ;1mrom 4500 rpm to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses383ngr6ew6cd tnve,d t *q ym* of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn thr*d*8vq63g36dnte wryt,c emnough 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 accelertvru :r0n4k*bates uniformly from 240 rpm to 360 rpm in 6.5 s. rrt*ubkv0n 4:How far will a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is runni+vkg9q)+-+sfovzuxya, h2;, k1cc q6cae p lmng at 850rev/min It turns 1500 revolutio; q c+,-g6xa2c z+ fsv1p+vyckq)aoku,lh9 mens 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 reduces its speed uniformly fz zkv8g++cj;l rom 95km/h to 45km/h The tires haj+lc;vk8z+gz ve 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 2 3m/7sfsfj n ym47),vbdto du65 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.80 m. ujbf s)7,styfdo2 3 /n4vd7mm
(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 5n0wrtz2 c8rt bike puts all her weight on each pedal when climbing a hill. The pedals rotate in 5nzt2rc0wt r 8a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of icy)*jekesmqm*mwe ;.-6 d n) a door 74 cm wide. What is the magnitude of the torque if the force is exerted )y m wmne6;.d)-eemc*sk i qj*
(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 tkx7y m0 zjuf nq-idks7y*: u- y3s3+ikhe axle of the wheel shown in Fig. 8–39. Assume that a frict*0km:yyfqx-+7sy u nk3-ijukz 7 d3siion 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 wh5yemmxge :0x*ich pivotmexxyeg*m 0: 5s as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightenink*c n5dxjc(: 4j isjl-g to a torque of 38 (xcl k j5s:jdjin*c4- $m \cdot N$ 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 mjp 4fd0rib/ 7e pw5j810.8-kg sphere of radius 0.648 m when the axis of rotation is tf0wp e 7i8dmp5j/rb4 jhrough its center.    $kg \cdot m^2$

  Calculate the moment of ing bgyc (14u-0*ucgwiuertia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ignored (whb u-uc(u0wgg1ic y*g 4y?).    $kg \cdot m^2$

  A small 650-gram ball on thnn vsn m1d(7sypxj0/. e end of a thin, light rod is rotated in a horizontal circle of radius nsp (yns7 xnd 0/mv1.j1.2 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 bow-u1b- ex sb0scwmz5) 6(qvep6s ok l0ul on a potter’s wheel rotating at constant angular speed (Fig. 8–42). Th-1vb b uqs-w uo ls5es6x(pk)m06zc0ee friction force between her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of point objects shown*kha+g0 a ksc7 in Fig. 8–43 abo sha+7ak*gc k0ut
(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 whlk6udlk03+05,9 p v- lv mgh zvrpf3w :nr+sgyose 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 correct ugud213 sr9 uwrate, engineers fire four tangential roc 1u3s2 ugrud9wkets 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 e9c (pnh/ut r 29etpj fgp*,q0of 8.50 cm and a mass of 0.580 kg. Calculate ,0p9p j9uhp*qgeet/t r2nc (f
(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, accelry8qxpv77ml7 nmghwz.e75( 1nlyom7erating 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 and if 1a98xf. i/f q,gmzpos 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 hasqg 9z 8 ffx/ompi.,fa1 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 rot.,q:an4bfqqah / m1f nating at 10,300 rpm is shut off and is eventually brought uniformly to rest by a fricti.n:famn aqh14fb, q /qonal 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 bt5cl ltu5q0nyz/bc1b ,y :jj7all 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 thrw 0c8jzb 2qc2ps ;lfe:own solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball iceb8z sc2wfl: qj;0p2s 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 co7 (pu9 xswu4a0*rf(fx9rd 1p7 bb axmdnsidered a long thin rod, as shown in Fig. 8–46ufx 1xdm7b(rw(9app b rfu79s4 xd0a *.
(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.    $kg \cdot m^2$
(b) How much torque must the motor apply to bring the blades up to a speed of 5 $rev/s$ in 8.0 s?    $m \cdot N$

An Atwood’s machine consists of tw4nent bj*: 7 azl*aqv,o 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 acceleratex*hcpq2i;jn3l 0yv2 hd42v xus the hammer from rest within four full turns (revolutions) and relqhn2puh*32xlv 4v ycxi0jd2; eases 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 ine93(q7bhjwsxn8 .p-fl iwa1fx rtia 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 tzar90m+ et+ azorque 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 raqtvc re5d ja8i8vq-is803k5/2koxcydius 9.0 cm rolls without slipping down a lane at 3.v/dxa c8oce-q0k yj5ii 83rkv 8st2q53 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy r/8d66 lpj4v fl gkb8dof the Earth with respect to the Sun as the sum of two j8l4r 6d8p k6fvd lgb/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 kg au1dg2c6m ohjn.ju)9m l8qly )nd a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylm1l 9j ghcj6)u.dq)mnl28yo uinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rim /; (ai/xnpjojg2b8est and rolls without slippinxo (/njmip2ij/ g;8 bag 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 verticall/fp j 3mhbw2y10io4asdko2 rj i9-)uyy on its tip. It starts to fall and its lower end does not slip. Whf2)w3opd9 -js 1iik r0 2ym/yujobha4at will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momenav28hjsr jt7h+68ic itum of a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an angular speed of 10.4 hs jav t7r6c2i8+ij8h $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform hnbr(mgslc: 1ee s, ujx0e2;*cylindrical grinding wheel of radius 18 cm when rotating at c;j*m,1e( hb0r:gleu 2es sn x1500 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 that46cb)edqo9l w3rtkg ; is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal pqbkldtw c6e9;) r4go3osition, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can reduce her momdff7h) mhho;9we09jjy(fa m *ent 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, j9yf97f 0h ; dhommha *()jfewwhat is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase h u6g5wsjy j,lkq* 02:ufs1djsu(jw i )er spin rotation rate from an initial rate of 1.0 rev every u6ulqdsgk1 ju w0jjf5) 2*(sws i,:yj2.0 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 thr t-cdas m vcj)7y*iy51ough its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 vy5t 1 *m)dsc j7-ycaicm, 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 7 :l-9ld:ij j/o(trda4q rji2d tlq7gof a figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentlhm d. oqf6nr837pw;h: nlp;sum 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 m; yo2zq +0zirds) h2nhoment of inertia I is dropped onto an identical disk rotating at angular speq)0 rzo; n 2+zysh2hided $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2. b hs8a9new aoe)m6w,14 $rev/s$ 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 rotsg spl* 3 lfw.)g(3qneating merry-go-round platform of radius 3.0 m andne*3 ssw qp()l.gfg l3 moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely with an anc0 zv pdzx j ;6g9/nklog m-yf5vxx*21gular velocity of 09/do 50l;x1 * vgk2nzcjxxm-gf z 6ypv.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 eventualujniy h5 9/5 fqb3k2suwbn-a)ly collapses into a white dwarf, 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 mos9 a- b/buyh25uinkj wn3fq)5mentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in excess of 120 i7 g;1m(8c r* m.om piqowfwj+$km/h$ 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 q 80d2 sx *drk9xlxph9d(t9 cc$ 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.rh m ,9qu7ief rest, that can rotate freely without friction. The moment of inertia of the person plusfmq97r h,. eui the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the ed0( 0z*)zujp9mwvh xhq ez,tv )ge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearingz,)ueqv*m (j 0 h vt0z9zh)pwxs 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 od53asr pbzv 8c;sb vw+i8m8 8wf 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 froi s5mwc3 8bdr8z;vbp8vas+w8 m the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same sid(i.g rs3zgc8h ,n/0xu7 zeou;q wx np7e always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) t. pi8hoz0c7(gzrw,/ 7qgx3nsuu ;xe no 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 m/qs4,57g9( (rz6bv;y i* p ubb,xygc ypod kxc0$s^2$ 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 ofg xo82t vnb3tiay-a(6 a uniform cylinder of radius 0.20 m acquires a rotational rate of nxt i2ao- a6t3v b8g(y from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disk7z lqc8r3.zga gjghd c 4oh.+( hp:3e6z 3knurs, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical c3h4hluk g3gg .oj .7rnzh8dqzr 6+epa 3(z:chub 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 angults2yl8 i:nznm 1pz c;wa* sx:+ar 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 wib05r(7 ttx6gk 5soe vdp7b(yl 2f,c1ct +azkwth mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational colla6 2+ektc 1bpsocta7vgfb (dktz50 ,l wx5ry(7pse 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 uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use energy stored .y- mia.7ned ityf q0.ea5 y:gin a heavy rotating flywheel. Syay0.ge dq7e. m.ti:n -5aiyfuppose 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 illustrates g2k:r.c wpx :kznk5 o7duh-n+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 surface at speed v=3lbvvus5p.3lf8:l2ms )wg3 j ahv.t3t.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 ign5ljgx*t9o( a3 r wow7ooq0lw5ore friction) about a hinge attached to a wall, as in 9aj(7qoxgo3l l 05wt*ro5o wwFig. 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. It is standinge l;v1 bkh 7wcpug 4mu/rs1.1j vertically on the floor, and we want to exert a horizontal forchj1lu/ .spwe1g 7brmu41 ;vkce 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 with speed v=4hxveqef 93he,5;w wl*.2m/s on a flat road is making a turn with a radius The forces acting on the cyclist and cycle are the n5h 9flw,e h3e;*q ewxvormal 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 +ej cs, +p.:gizo /nzbm and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and wh.++bjnspi /: ezocz g,ere does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms )d 1+mb.w4j+3 zcq ed6rtkvv30j ztucas thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds dzc1. t63 bt v 0)r4z3q+dvmeu+kjwcjfor a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly wlwaga-bv*.) eun x pqh0q0/ex, *be2 dhich consists of two cylindrical plates, ofaq h0./*a -ux 2eg, weqn* xbvled0p)b mass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 loo nssq/8m;it 9cped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must89i ctssmn/;q 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 assume nmu62 u s1w;nb$r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed uniformly fr+ 6yhmpiu,mo n8g/s/v om 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration vuos,m6hmypig/ 8n/+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