A bicycle odometer (we4u57sf zv.mm hich measures distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you 7uvs5emz.4m f use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velt auvyl/ c6,/5vu:hdtr+q ri 1ocity. Does a point on the rim have radial and/or tangential acceleration? If the dis tlu5r:q/vhc6+ uytv1i/rd,a k’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 be desc qwd,.nfsta t2nuz78 4ribed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greaterx5.haekf2zned62xj gm - 7+tu torque than a larger 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 yohtk uyxq) jf:55v9td7 ur head than when your armsqfdvyhtuk7 9j):t55x are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the 8bdhtom:+ r,r3fle7 vrear 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 a8b ,tl dvhfe+ 7mr3o:r large front sprocket? Why?

Mammals that depend on being able to run fast have a3u -mnf ;u(hcslender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–3cah fmun(3 ;-u4). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–3kzv1xq;8 zhp xd61/ yg5) carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If the nef/,j fra jw +fg/2vje0t torque on a systej+//gv2 f0j,eafrjfw m is zero, is the net force zero?

Two inclines have the same height vn/jd9a n*5px4b / jbbbut make different angles with the horizontal. The same steel ball is rolled down each incline. On which incline wi 5bn //9nxbj4a*d bvpjll the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rpkxr7stjbnk m2t9ng. 68 9s4wolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which p4jns6s8brxm9 gnt. 9tk2kw 7reaches 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 r/syjlnez9k39 adius and the same mass. They start from rest at the top of an incline. Which reaches 3/yk9ls9 ejnzthe bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and anguk+bfe3w j3fp 2lar momentum are conserved. Yet most moving or rotating objects eventuallyw32+e fb3 jkfp slow down and stop. Explain.

If there were a great migration of peeez85 lx(d :oxp, t/viople toward the Earth’s equator, how would this affect the length of tv8:dx5e ptl, z/oi(exhe day?

Can the diver of Fig. 8–29 do a somersault without having any initia; 4ht ,va8i 5;aukc+xf bctb*ml rotation when she leaves the b;k;,8ht +4a bbuaivc5*tmf cxoard?

The moment of inertia of a rotating solid disk about an axihdf(ib uuon0l 92 hs)bp96 nb8s through its center of mass isf) 2hdp(6 nl9ub8bs0no hiub 9 $\frac{1}{2}WR^2$ (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 rota.bt zh66rfxe 9ac5-px ting stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, debzh 6.rpcx9-axt65fecrease, or stay the same? Explain.

Two spheres look identicacgfp 4f/fwaq 78d)4gs l and have the same mass. However, one is hollow and the otherfd8p scf f4w)/g4g 7aq is solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal a6ror d f stu)ctp,t,/+ o*5va4uqwlv.xle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasin,+s5 wvuu .pt6rtaocfd/4qtv *l,) ro g?

Suppose you are standing on the edge of a large freely x ;le8j wi: jnu *a du*xn98ro8lq;,pbrotating turntable. What happens if you walk toward tor8x 8bw p:*ud* ilujj,;anqex;n8l9he center?

A shortstop may leap into the p vsude0ac,wg))xxqh-,;7 i1ys; spw air to catch a ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly youh),ypdp;cqx)u i,s0saxw ;s- vw7 eg1 will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular mou/brhu j/ 3hvvp7h8j :mentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operatjub3 h 8urvh/pvh7j:/e to keep the helicopter stable.

  Express the following angles in radians: /n7vbu0j d 8nuiph: knp4bb4)(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 o,hqxof6+n a7)q;* cq mahk g)bf an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Su )ab6 m;nx)cqq,h f7g k+a*hqon and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km frost 1sbu.nd+6o(yjpz 1 m Earth. The beam diverges at an angynp(s6osdz1 1bu tj+.le $\theta$ (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 motor ishp8 gih)z,3 fe turned off during operation, the blades slow to resth3efpi) z ,g8h 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 brygb(z*nie5x-+; 3f kwe2hafloor 3.5 m to another child. If the ball makes 15.0 r3f;b eyk nxr*5z+ (higebaw-2 evolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolut:pkllin4tkd5 ).1u qiions do the wheel1u q5i nldkip. tl:k4)s make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500shz 0 te/x6mi w99g6jf rpm. Calculate its angularh6m9 ji9feg wzt/6xs0 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:kybhx8nco/lt: ,z 7r complete revolution in 4.0 s (Fig. 8–38). (a) What is thex8ry 7/c:bnh,to l:zk linear speed 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 c2lvhle* .- udph+d. bEarth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed/+x8zfg yhe d4 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 centrifegw6x3il 6/ h-gq-gz cuge rotate if a particle 7.0 cm from the axis of rotation is to experience an acceleration of 100,0g-63gil e-h cg/zx6qw 00 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from m93h r,xyn (3jhsgo dllx62g:130 rpm to 280 rpm in 4.0 s. Determojlrn:9m,g l3 d62yg(s3hh xxine
(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 radiuuj+9:eu8 rvmki4zyh2 s $R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$

  In traveling to the Moovxg, pitm t,gsw9+;tq* ls: 9)qg*hzqn, astronauts aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energyg*s w 9g*:,ptizl)9;sm tqvh+ t ,gqqx 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 unwh3ezcyalm ; c:5d9p/hmj y 17z 58rtgiformly from rest to 15,000 rpm in 220 s. Through how many revolutions did it turz5: gcy9/pdc rtem7lh yj a3w z8;h15mn in this time?    $rev$

  An automobile engine slows down 4knh+9chug1 m+ k.phv from 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 stresses of flying highmd7yi yg f:g70speed jets in a whirling “human centrifuge,” which takes 1.0 min to turn throu7i : gy70mdyfggh 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 acceleratyqooc (va0zji4*cqkcy8o fk 7:rh-; 0es uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the whi(oo qy7*a fzjckkoq y;8 -c0cvr4 0h:eel have traveled in this time?    m

  A cooling fan is turned off when it is runrjbu bi71f7n9 ning at 850rev/min It turns 1500 revolutions before it comesjb rnf97bu1i 7 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 0wb09ix/elov*5r b jj car reduces its speed uniformly from 95km/h to 45km/h T5v e/0 *0 o9wjirjbblxhe 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 its speed uniformldmah://b9umg0v sc9pl/l 3 oky from 95km/h to 45km/h The tires haveb vu9/0gm/mcpl d:o/kh9s 3al 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

  A 55-kg person riding a bike pe9(rbu f/ao c:uts all her weight on each pedal when climbing a hill. The pedals rotate in a circle of radius 17 cmb/ro eafu :9c(.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force o;u0hh 1sk;jl qf 55 N on the end of a door 74 cm wide. What is the magnitude of the torque if the ;1;hq l0jhskuforce 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 torquejz h+ah x7dz0/ about the axle of the wheel shown in Fig. 8–39. Assume that a friction torz7 /j0hdxa z+hque 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 which 6le++84.eyx 3vjqc1r xinl +nrlav,mpivots as shown in Fig. 8–40. +riexnq.,al + 1r 6cvnl3jv 8e+ylmx4Initially 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 a29 ob- 8u0huzdf6yvf an engine require tightening to a torque of 38 8o0f-af b9udv6zu y2h$m \cdot N$ 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 radius ra;z gdvdee7 )5x *pem53f +hm0.648 m when the axis of rotation is thro *53;h7 eer+z mfxd)p5gvea mdugh its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7,oe2 2rlncrm.y,6 fpv cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hubymr,vf6ce l2ro n., p2 can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in,9xk5erzkkge5 a,2d d a horizontal circle of radius 1.2 m. Calad e9z2, k55kk r,dgxeculate
(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 xajugzr6, 5b4 bowl on a potter’s wheel rotating at constant angular speed (Fig. 8u, zrb4 jx56ag–42). The friction force between her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of bxk97k+9b5ms6xxpfo/ g bq9d point objects shown in Fig. 8–43 abousxx9x ok5+kbpmbdf 9/ 96bqg7t
(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 atomvp ,uj .g61g4kslf+ yws whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning at the7 n+j*xvbd1cdhv 2 w kr.k0.a0e; wqwu correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to re0*1.veqh72k ua bjc d+w0nwr v; .wxdkach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a ugln2; e m*,qcuniform cylinder with a radius of 8.50 cm and a mass of 0.580 kg. nleu* , 2;gcqmCalculate
(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 to 3hm1 ujr;vp ru( slw:d2uz .*;i $rev/s$ 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-gb viozv7(m2* jvs;rynys2. (c o-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 as yzms2v 2b;n*. ocjyv(( riv7 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 rni:4fzpp si, ,bapg- 5otating at 10,300 rpm is shut off and is eventually brought uniformly to rest by a frictional torque of 1.g :ippp ,-5f abi4,nsz2 $m \cdot N$ 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 ncq5p dkpp0tok g27n81vr-z0 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 throwncs0 +blsfwgjeiy77-2 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 is albgwi e7-+cssf07 2 jyccelerated 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 shay pre,c+o)x*qf 9thv 45lt) bown in Fig. 8–46. b* l,cfvo)4 p5y)9t+e qha xtr
(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 consistsex/m)*x,lnst of two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest 6*dkdnwk-o)r within four full turns (revolutions) and releases it at a speed of 2 kod wd-6)r*nk8 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of inertia of :nub p de;)hf7 rf czc;3te *8rsbyl6,$3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a to8bo+fjxqmt*wd16 1*t f v0m ugrque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls without slipping down 95 m8 m+w 9 wsrcj /dycuq5u,pcltpz4tmc-).ia lane au,yd54mwmcp8m c9c9- c)t wr5qzj. pi/+t lsu t 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to 0ordfadp; 7ep* p(7qro+ ij0cthe Sun as the sum of two terms,roi7f0 c0oe j;rp7qp(dp+d*a
(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 16bji s-+sfzq3h t ;e;2gki 2y8e0 gbb9l40 kg and a radius of 7.50 m. How much net work is required to accelerate it h j8s; 2 e+kl;0 i2bg-qz tgysbfib3e9from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg r6t goycn)0 2sstarts from rest and rolls without slipping down a 30o6)0 y2trngsc.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 :x*p ljae .e7mvertically on its tip. It starts to fall and its lower end does not slip. What will be the speed :xja eelm. p7*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 of a 0.210-kg ball rotating on the end of a6as lp(x7jr5 i thin string in a circle of radius 1.10 m at an anj( is6p 5rlax7gular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrkww, *x 1w:o(i-uidozamp m*1n odo-(ical grinding wheel of radiozo(n:u*p 1d m owd --w k,1(oxai*wmius 18 cm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that is rotating at a rate of+f)o g++4:istxv ,umq 4ut omw 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decreases to 0. tt4q4w+m:ofxi+sum ),vo+g u 8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig:w*,e+ yud1b fnhhia4y zv+:x8e; kzn. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is f:y zdw+:a1hih*n k8ex ,ubev4 +ny;zher angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial rje :bth59 vh9mate of 1.0 rev every 2.0 s 5htb:hv9j9 emto 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 zt (a*j,ys. wjfrequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to i ty,.ja*j s(wzt?    $rev/s$

  (a) What is the angular momentum of a figurevlx , e/3abqa( 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 mom5typ2lcbvo 2)dib 9/b0wn x2gk50 fkientum 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 f*o:2kvo(y q odropped onto an identical disk rotating at angu(: ok2* qyofovlar speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns apdhn8 yuig/ qbv;)6abl,*)dw;xv g6 5 (zpo lat 2.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a r dx4 fj4s/;, u.0arzek pp2ihcotating merry-go-round platform of radius 3.0 m and mom. 24x0ae; sdj ip4z,k/rpuhfc ent 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 ixw*n ao67jb5hpxx tvd 3p4x3/s rotating freely with an angular velocity of 0.8 a3 dwbpx nt4 /p5jx7x*hv6o3x$rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a white dwarf, losing about half its ml)hhw;uu/to 5ass 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 rotation rate be?(round to thel)h/ u w;hto5u 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 invol:vox4tibd(z atx* m7 oe7a ;3mve 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 ))f l 94/a6vu0ktv y oslu)w5zcxk( dqk7:rxu$ 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 atw;r l(f8sq w+)jo bvc2 rest, that can rotate freely without friction. The moment of inertia of the persoqvl(f )2co8r+;w bsjw n 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 sta1ot3 gx*)ogab)9 wtqinds at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearing3 *tgqoibw x)91otga)s 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 tisbg 2f t-e *gwgz3*;yhe rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s centeyw-3 bti 2sge;ggf*z *r of mass move?

  The Moon orbits the Earth such tharwa/4h 6;gtdr t the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latt4ardh;r w6gt/er case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of stbz jda85+y3 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder zlor+fc s)e: wo:z9:wof radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular accelerfc:zo+wsz9) :w eolr: ation. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, ea) rcdzvm yob/.i-s8/ech 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 it reaches the end of its 1.0-m- -)odczvy8rsmb ./ie/ long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, hok*boa f61mbktz k ly:07.ikn-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 4m2fqn.*rnauvn 28vh/tw5b q Sun, but 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 rotation speed be? Assume that the nr.vtw5m2/q2u*n havq8f 4 n bstar 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 autommm 8i+ fu-x- )sd(;dcbe, rdt0r (jthfboc.k (obile is for it to use energy stored in a hmi+e dx(;8 mj ft(c.fdc-o bubs0kt -,(dh)r reavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrates an z:hvxh vvfb*++*b )v xvl;j q3$H_2O$ 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=3.3 y9-owo /vg:eiazs(lba-; j0o$m/s$ 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 cang trifh*r (*o* pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of rht* r*gi* (fothe rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on the f+wsne,zzd 0 2y+jiqhyp/n,8rloor, and we want to exert a horizontal force F at its axle so that it will climb a step against whicq2 hinejn w+/r,d pz8,+0zyy sh it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed0slee ;( bm+wigrd04f v=4.2m/s on a flat road is making a turn with a ra4w egli+fm( ;s erb0d0dius The forces acting on the cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling(f v: nwu* s(uqm/vh:n of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerat:f( qu: n(v huwsvm*n/ing it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as t;n zxbj9xq 2t5hin rods, making rj x5zxb29tn;qeasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assem .o) 8chfwekr*mwp.l(bly which consists of two cylindrical plates, of mae(ohr..pkw* lw m)8cfss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 mgr ek9 nj)b77dehs(yg9(0 tfrolls 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 fg0(h9 b79gmjrn7ey(e )tsk dis 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 do8 fdan oxdpd u w).yfi7u42m-, not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85e 05x kvv)c .6y8/dbg9nkyyvr revolutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. x gv/ y60v9y)8r ynd5 cb.ekvk(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