A bicycle odometer (which measures distance traveled) is attached near the wheeloc:.; y l2gatykjs :q1 hub and is designed for 27-inch wheels. What happens if you use io; 2 ksgatj1l.c y:yq:t on a bicycle with 24-inch wheels?

Suppose a disk rotates m6r t2) 8vixgkf3 w9yiat constant angular velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the poiwmfyt3x 89gi2 6)kivr nt have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the angulagu 3n7jhgek8, r velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger for 5f/3wo3vqsftce? 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 han4jb) b3.*zjeeo7 tfr7 buzs c6ds behind your head than when your arms are stretched out in front of you7ce r ue46.j7bb t)*sz3jfbzo? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three )3tl7ctavo cuc x( q2-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 p tqavc3l7 -o2 cxu()tcedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lowerl sqls8 qxzer8.o f*2( legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution e(o 8s.zsrx*qll2 8fq of mass is advantageous.

Why do tightrope walkcue:v8f5jj 50isl/y vyg*s v)ers (Fig. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If pn85jgywsy3) 8; x 8alrwdd:jthe net torque on a system is zero, is gw 8pd8ax jy;:js5 wr ny8l)3dthe net force zero?

Two inclines have the same height but make different angles with the horizontawwsi/zb t6f,(ep az)t( 62lgsl. The same steel ball is rolled down each incline. On which incline will the speed of the ball at stb6gsap (e2w z6 itlw (f,z)/the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an p) +5-sakk/ms cs)s whsmcp ;1)rx:*djmaw 4eincline. 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 k epmmcms 1wpj s*+:dc-srwkk)s5)h4);a/ xsa inetic energy at the bottom?

A sphere and a cylindv3n f-hqi528 3m5gxzhmg* pncer have the same radius and the same mass. 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 greater 5-v5f m2 gncg3h* pzmi3nhxq8rotational KE?

We claim that momentum and angular momentz fik0v4xej+)um are conserved. Yet most moving or rotating objects eventually slow downf 4+0kej vz)ix and stop. Explain.

If there were a great migration of people toward the Earth’s equator, how wouldg xqym5c47xgim:8h 0t this affect h0q gmg7tx5x :4cymi8the length of the day?

Can the diver of Fig. 8–29 do a someuocn ;ng,wbz 3w t(-e)rsault without having any initial rotation when she leaves the board? -e(, nwcbo gnw )ut;z3

The moment of inertia of a rotatingv*okifuc5b 2* solid disk about an axis through its center ofk2 cfuo*ibv5 * 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 sb* o5 ,sjr uw58wjewk9tool holding a 2-kg mass in each outstretched hand. If you suddenly drowkwje9rwb *j8s5 o5, up the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have t4uhs xlf7.e cs -p5(jthe same mass. However, one is hollow and the other is solid. Describe an expex s7 4hu(eflctpj5-s.riment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axlee tew7yx 656xgj o/2sp 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 tyt 7o/xxwpg5ejs6 2 6ehe top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a larx+ u/e:i i)eesge freely rotating turntable. What hap)+i/ ee:uxsi epens if you walk toward the center?

A shortstop may leap into the air to catch a ball and throw it qui0qxceg6km ( 805 nmkjlckly. As he throws the ball, the upper part of his body rotgk05k6 0jmnm8x elcq (ates. 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 lam2/6 xkuko pc4w of conservation of angular momentum, discuss why a helicopter must have42 uc pkk/6xom more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians: (a) 30 u73wumsw sd** $^{\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 coincidenci*8q(:wn-le g3zqm+i:z nit p e. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on:- nq mzlp*q+8e:gz(w 3iit in Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. T9z0che ig04 t7zy4 vvzhe beam diverges at an 40y47 zhz9i vzcvtg0eangle $\theta$ (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 dff.r. fxd+3s 4y;yo-.shbvsrate of 6500 rpm. When the motor is turned off during operation, the blades slovff.sdr.os y; 3+xfsby. h4-dw 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 another child. If the bal+cw(c,,ygk; esool l(l makes 15.0 revolg o l(kc oew,y(,+cs;lutions, what is its diameter?    m

  A bicycle with tires +m, ryoh5xo0b68 cm in diameter travels 8.0 km. How many revolutions do the wheels makeb50+ox, mohry ?    $rev$

  (a) A grinding wheel 0.35 m in diameter rogthx*vrsud17 eo9.)yx :4wprtates at 2500 rpm. Calculate its angular velocity in p d17ur9ov h r 4xst.x)g:wy*e$rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolution in 4.0 s mgtn)eg,s kl4 kfb((f9ed 31j(Fig. 8–38). (a) What is the linear speed of a child seated 1etfke41ld(3 fb )(skmn 9gg,j.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 5rqaw1s/:wcpy * c, qsthe Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear sf 5ylh f0;ear8peed 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 j,wbpznkb4t bt (z-:/7tle; drotate if a particle 7.0 cm from the axis of rotation is to experience an acceleration wzdbb:z 7;,(nt /ktj4 lte- bpof 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from pd 5jjb5s6ey23-qkm+ 5fkxiu130 rpm to 280 rpm in 4.0 s. Determine yj 5bf-5sq6kdm+2pj5i3kxu e
(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 radius0mw if1rs(4l p $R_1$ 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 0y1:qvlkhq2e+*w.y *h lhzrcaio4 n 2im:of (Moon, astronauts aboard the Apollo spacecraft put themselves 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 spacecraft can be thought of as a cylinder* mcr+wn2 ylk*e(ofly. 2:v4 :0qa hhzhoq1ii 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.al3 f md ruk1z-vi,uv6;;fqc* Through how many revolutions did it turn in u6 -c3u1 dfm*l,irqz;fa; vvkthis time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s.jm*sx/s:spj mc o /c4 n xe2wc3:7d0pt Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jets in a nt j a5z xh7w9wv0(yt(,+1mvavm p iq*whirling “human centrifuge,” which takes 1.0 0vt ,+m(ya(z i w9*xvahvjp7tw1 5mqn min to turn through 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 rpsgw :isx mc*7k jr:;i-m to 360 rpm in 6.5 s. How far will a point on the edge of:gm wiss -xr*: ;kc7ij the wheel have traveled in this time?    m

  A cooling fan is turned off b:h0f 1*raj fjwhen it is running at 850rev/min It turns 1500 revolutions befo hf1rjbf0aj*: re 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 reducell 8h3d r,h:ow2 ,bknvs its speed uniformly from 95km/h to 45km/hlwb ,38 :hn v,rkl2hod 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 revolutions as the car reduces awtq+ut(q v/+q6ty9 -m m8wd sits speed uniformly from 95km/h to 45km/h The tires have a dtt uw -m/+6q w9q+ty8aq(s mvdiameter 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 he(m2 5fhb ipo7zr weight on each pedal when climbing a hilbmf i2(7hozp5l. 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 the end of a door 74 cm wide. What is hin23wgs uzsnw*0:0n95 ds ab the magnitude of the torque if the force is exertendhs0ssn i3uw0 za9 gw:bn52 *d
(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 aboutv6jnl 2,aln7di+k nd9,l3 rbt the axle of the wheel shown in Fig. 8–39. Assume tha,+ 27, l9ldtv 6nrnb3lknajdit a friction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a massless zja tal-h;,bfvm 3w/+ rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnit;la w,jz/a 3+-h tfmbvude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine requiri 3hn,.vf azv4kglp u-1mjz (+e tightening to a torque of 38k -+u,hizj4nz .(3l m1 fpavvg $m \cdot N$ 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 inertil)4t aiqju;arl ,ntxp. w:/ 0wa of a 10.8-kg sphere of radius 0.648 m when the axis of rotation is through inl)0rw tj txp;l. qai:a/w4,uts center.    $kg \cdot m^2$

  Calculate the moment of iner1yr v rfc kace,(9 6.on*sqgq7tia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The masy 9* c.s na7r( gqc61oqk,frves of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in a horizonta/kd 1a h:v6s hp+kvb w5wp/w2tl circle of radius 1.2 m. Calculat:dwbkh //+vtw5hp 1sv6ap2w ke
(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 wzq x 5 n2aa,lp/plfs(uf1s)dz7,v(e dheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and the xaesa1l ps(/) uvfl27,zd5z(f pqnd,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 z i gu ac(.u0b;65wwtyof inertia of the array of point objects shown in Fig. 8–43 a z 60. ;awi(gtu5cuwbybout
(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 atom: pu 4labf/fg:s 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 spinninv1/ zghe7;v -o7dziufg at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is -1/zuhovde fvi7z; g7to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius oxhrq1 im07*nwo0oh m -f 8.50 cm and a mass of 0.580 kg. Co-xo07 nrhq m*10 iwmhalculate
(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 f2yeo8gl d/pha/2a: m6/y z pjcrom 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 lbq9( w)vpi(kd n4 7gja small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg(q9gd (plj)nbv w7ki4, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is eventually b zbd ks41i7csy2-eif8rought uniformly to rest by ssd17z-c42ybi ike8f a frictional 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.q9x xs2xz . exl30z1 ny lyh/yzeq3b/-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 yq3d.h-c;tf hzm ujj-. qok c- 91.xbpball is thrown solely by the action of the forearm, which rotates about tohc3tmhcyj .d u..-fbp -z qk; xq1j9-he 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 considered a long thin rod, as shown in 6t6sg6r +r fwnhhhs 8.Fig. 8–46n86hgf r6 .wssthh+ r6.
(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.    $kg \cdot m^2$
(b) How much torque must the motor apply to bring the blades up to a speed of 5 $rev/s$ in 8.0 s?    $m \cdot N$

An Atwood’s machine consists of two masses,(27z oh/yn7s: c3lfjxvm 9f ee $m_1$ 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 acczb ca ;uhr8t/.eexd8 /elerates the hammer from rest within four full turns (revolutions) and releases it at a speed of 28 u eh;/8.brxt zec /a8d$m/s$ 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 had;m*z,sug2kf nj (ozv)jkn)4s a 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 develops a torque of 2w9:7powe as1 *m p1ymq46ghny80 $m \cdot N$ 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 sf.3)yw 9*(rez:gtjfzx6io g k lipping down a lane at 3.6kf3(g:x fg w tozi9er *)y.zj3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun a4jm ,3 b3kiyue o27a/.tkepnes the sum of two terms, uk3bk/a ep32ye,jne.mi 4 o 7t
(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 jpd4s(: gpre3 mass of 1640 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation raters4ep :(j d3gp 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 br v .qn((dbjc2egb0q1qc. +q kg starts from rest and rolls without slipjvegq(q.q bbr 12c +n.cbd0(q ping 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 bala n fa8bnx6n q)7tl4d. f*qtc,bnced vertically on its tip. It starts to fall and its qd.na*b)n,ftc4f7nqxtl b68lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum ofu zjaurk1-1j4 a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an angular spee-zu4 1ajujrk1d of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular moment;4i ikwk.ql :5 bel86boi5rdkz3bez ,um of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotatinizk6ikqb4:ld58 .5ib ,be k;wlz3 eorg 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 rotating at yum kw:aftn/53+zg0g a rate of 1.3revk 5y gumt/0w:n+z 3fag/s If he raises his 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 cpa/ 9rfl3vgpju91-o -vkt6 xFig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straightkvc rx1vuf6/aj - 3glp-9po9t position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increaseh al (lfhr5u12+ arga, her spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a hu r ,1+5laa(lr2aghffinal 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 atnf9unvfl20r6p;o o 7km4lk2i a frequency of 1.5rev/s The wheel can be considered a uniform disk of masn; 926plu mvfrki 40nok2ol7fs 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 x ,;o*fo(3 *lfwgsir6gobs j+skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of t eou-rl.5kv0 zp*;psc he 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 in qgu 98jr07*rynxtwidp+s):oertia I is dropped onto an identical dix8tw7pg)nrj9dyq s u r0+oi*:sk rotating 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.l*wp4 5.aun q0ms zs+z4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating .mryd- 7))fi 5-snnma8hcz4keb2qtv merry-go-round platform of radius 3.0 m and 4)v-r m-ebq mh n7)t25f.an8d iycs zkmoment 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 angular velocity2 )odh;/1h541flmswkj2 xtp i np v7ez of 0.8hpspn51mk2ed /itf 1 )zj wv 47x2o;hl $rad/s$ 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 (xvczp;7e9 o jwhite dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing rad jzve7(;c9 pxoius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in excess of 120bvlyg i ;f:x.3 $km/h$ 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 za411n7f7f 5;slm 5e,hgss7xwh kfnw $ 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 rotate n u ogh.xwl*lp*8 xk/5freely without friction. Theho xk luwl8g/*p*.n5x moment of inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of 3 mbiyshe3h-.(apli *ycqz:4kwd 8d4a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a m8m3h d-*3w. i:4ady lhc e4k(zybpqsioment 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 gwhmw;mftj0r o(qw0- / round 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 rolls behind the person without slipping. What length of rope unwinds from the spool? How far does them0rw-;oj wfwqthm /0 ( spool’s center of mass move?

  The Moon orbits the Earth such that the same side bi3,/ j +u hacjum3tj5l6dz7 galways faces the Earth. Determine the ratio ojj6b,/ih uu 33gdl+z5ac tj7mf the Moon’s spin angular 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 m2/:s kkltjf+vi13r kxe;l /k 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 ofeg6wi:zku3:dba0v k+( if3kp 8*u oyq a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s intervaluqk e :3:bo+yvwi80u pig(* da 3zf6kk at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.050 kg annpgh 4pt-i+-rljv5t hua; 3x 6mnr-, fd 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-n jpp5tltg;n- xu -f6ram4rvih 3h-+,yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the rnx 4ka pm 1c.w ajeug02p.3m.gear 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, buc( xz8; s3l1fikrpftq 70+ olut with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its roto 8c(kr1l q73;x0tzu +fflp isation 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 qkzafa5 u : l5vp+i9k+stored in a heavy rotating flywheel. Suppose such uz i:lk+qka favp5+59a 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 illustraf fp98h -+xmln,3qo-w*q lpcgtes 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 e diz-o bc+(q2e,e4csn( p8ka 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 andal)re5nk:ucib2,4sw. th( w f length L can pivot freely (i.e., we ignore friction) about a hiiu b (cn rs5hta.kfl4we,w2 ):nge 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. It is standing vertically on the floor ru0soxw4d +4c, and we want to exert a horizontal force F at its axle so that it will climb a step againstxwd or+4 0s4uc which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is making a turn wrymw45 b;2lrxnscai4 4hvx74ith a radius The forces acting orh2nm4acis4lx;74 rxb v 5w y4n 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 inta7 dtob1l -sj55s7*iow h uy3ho a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from 5-hi5 7ys7wout*s1l jba3 od hrest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thin rods, m kt8ifr4luq70e gy)/a aking reasonable estimates for the dimensions. Then calculate the ratio of the aluga 7) /8efrkqt iy40ngular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consiy l,wvb/ zwm1(sts of two cylindrical plates, of ma ybm,1wvwl(z/ss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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- aut1eqww97d 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 highest pw- qde a9t71wuoint of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not uglm nt7 3t, k7 t3e r+arbwj33;1mqjpassume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car redunei-fs u.0 l,gces 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-,efs 0.gli un 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