A bicycle odometer (which measures distance traveled) is -.wcdd -)bmw had: 8 ivu86fkyattached near the wheel hub and is designed for 27-inch wheels. What happens if you used)d.u wm vf-a8k -iwy cb6d:h8 it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on the8z ys/ fsa4is/ rim have radial and/or tangentialzs84i sa/fy/s 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 be descrc9 ;dc, napwwv(jdj( :ibed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a grwzb u15 ld1.hgecm*z 6eater 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 your head than nn or6ube i.1q -13bhnwhen your arms are stretched out in f.-311nn o r eqnub6bihront of you? A diagram may help you to answer this.

A 21-speed bicycle has seven spr-pua azb l)3sy;+ 0psrockets at the rear wheel and three at the pedal cranks. In which gear is it harder to peb y0s3-slp;)z pra+ua dal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower+sferbqv+5 eof p.o 3, legs with flesh and muscle concentrated h ,ov5+ 3f +sbro.efqpeigh, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow bej;fc(l; qmv-e8h om)tam?

If the net force on a system is zero, is the net torque also zero? Io lnkrfa+)en4k*l)i3:4 wb puf the net torque on a system iob frn)+u4k *4 pial ln)kew:3s zero, is the net force zero?

Two inclines have the same height but make different angles wita:l5bn g**kt zh the horizontal. The same steel ball is rolled down each incl : 5t*algbkzn*ine. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolbp ./.mrag 9axling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottrg m/bx.a9a.p om 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 ma d + fduq:/9ws1dstkr -a:usd3ss. They start from rest at the top of an incli1d w/9ds:- :qdfk+ruu stads3ne. 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 rotational KE?

We claim that momentum and angular momentum are conserved.ax 2)7vaih m 3mim*:hj Yet most moving or rotating obje)iavj*mxhi:m3a 7 2hm cts eventually slow down and stop. Explain.

If there were a great 1 l8wk pvx*afh); -z4lkmrdg 6migration of people toward the Earth’s equator, how would this al k1w64zkv-mlxafp8dgr* h;)ffect the length of the day?

Can the diver of Fig. 8–29 do a some knni(g/f 8i4zrsault without having any initial rotation when she leavi znkg/ n(f84ies the board?

The moment of inertia of a rotating solimxp :fqs)ao +;d disk about an axis through its center of mass iso;p x+s) fqma: $\frac{1}{2}WR^2$ (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 8h wvs,5pj gs,holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase,, 5,whvjpsgs8 decrease, or stay the same? Explain.

Two spheres look identical and have the same m;)r b 1lw-3zi3,+lne.dc9iltczl nl gass. However, one is hollow and the other is sowtzlclil;llnd)z1e gic -nr39, 3+b.lid. Describe an experiment to determine which is which.

The angular velocity of a wheeq 7.w;gi0m+0p,ct gv w8r whtul rotating on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular accelp.cr+wi7 8w 0v tu,0ggwhm; qteration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating turntable. Whk6*m b(sxhi i1at b*k1h6s(i mxihappens if you walk toward the center?

A shortstop may leap into the air to catch a ball and +el:ynu +b3na throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opbnua3+ eny l+:posite direction (Fig. 8–36). Explain.

On the basis of the law + 21; 8(sb.upebi r(ptqpzz+fce dla .of conservation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter staba(1iz2e +b (sp8cbquzpd.re;. t+ lpfle.

  Express the following angles 4owow-p1b cz3ox *3siin radians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coincidenceo4rvz tobu +)s hi+(5l. Calculate, using the information inside the Front Cover, the angular diameters (iiz+(tlo u54hr)+ v bosn 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 t5u3m4ldeyj* k9ecd1f c/g tq-9vw k4km from Earth. The beam diverges at an angletk w3ue-cfc 4 lykvdq5ejd49 9/ m1*gt $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blendom /ljt8: 5v1idw llo+;bfh*xer rotate at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest ;8mvlotl* +h wx/b l :f1od5jiin 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 ballg),s(gkp45t zeu ssl 8 makes 15.0 rels4se(sz t8 )pk 5u,ggvolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels6vpb;fm g4g q6iid 9o,is.mk 9 8.0 km. How many revolutions do the wheels mg6 qs9v;imk.bd4mfo6g p9,i iake?    $rev$

  (a) A grinding wheel 0.35 m in diamgm6(tx,j /u oketer rotates at 2500 rpm. Calculate its angular velocity in muokx , 6(/jtg$rad/s$ $\omega$ =    $rad/sec$
(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 compndyx6 e;qyz w;dq knnx.57og3x1+ g. jlete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m 5w; kq1x76gd qn;+yyn dx.zx3jgo. enfrom 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 E79tnzz7ngf d91 :gook rw -+z/ ub1fpaarth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of ag5 b8 ev 3fpl7u 38govk;haa+n point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a parti a)6 dme7fsm3 xfq.1hr;e vqj2cle 7.0 cm from the axis of rotation is to exper jem)x2dq6 3 ref;hm vf7q1s.aience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformfv u ,+ e3q7s)xu/+ dfryj ne1dteiw,4ly about its center from 130 rpm to 280 rpm in 4.0 s. Determine + r unwusv1e/ef)de i+,34q7tfyd,xj
(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 1salu/w0q*l 6v: cah k$R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$

  In traveling to the Moon, astronauts aboard the Apollo spacecra4h( ynzazwk8*y7 z i5t mln+8lft put themselves into zn8t (ahm4 5z+ny7z8lwlk y*i 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 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 (x ltcu18qp f(from rest to 15,000 rpm in 220 s. Through how many revop( fqxutc8 1(llutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Cal-hoj4g bb2obk,4+u psculate
(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 strex 5m+0-np 9naq,ute udsses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before r9uutd 5n +mxe-np a,0qeaching 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 rpm to 360 rpm in 6.5 8 9ax2fskw7pss. How far will a poi x9skpfw78 s2ant on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 1500 rezt8b iwt4e hb4*v x.(yvolutionsh84.t4t xbbewy( *zvi 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 rtv32s( nk5sm 2ybh,m mxk5bc6evolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have6cbbh(, x2 mknv5s2 tk mysm53 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 re zzgl7y s.0)j- ud:y -tpmmtr3volutions as the car reduces its speed uniformly from 95km/h to 45kmrt0y3t-l .y7u j mzmgd-s)z :p/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on each pedal when climbing yz z fxf7wt4nu/7w96ba hill. The pedals rotate in a circle of radius 1/7xz6 4f b7nuftwwy z97 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force/0dnqu87 2s. ivmvfrt of 55 N on the end of a door 74 cm wide. What is the magnitude of the torque if t7.u/2nst8r qviv df0mhe force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the:*;ppj0ef/r w5e ,dxwo j6eb.uro3wkiyb, r) axle of the wheel shown in Fig. 8–39. Assume that a friction torque of 0.4wry;3fo0 ,wr d*j:5eo eejkp6biw).u p/bxr, $m \cdot N$ 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 pi g1*17xdk2wuuuof5ax vots as shown in Fig. 8–40. Initially the rod is held inxdxw1u7 k2u5*1gfuao 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 tightening to a torque of 38/mjpc,8(4;vr oz cgfc (mzo/8c,v;jrgf4 p cc $m \cdot N$ 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 0.648 m when thekf llu,46s*xp , k75hopihpp2 axis of rotation is throp kf ,5*xs h7p 6oilukp4p2hl,ugh its center.    $kg \cdot m^2$

  Calculate the moment of inelwk .*fx5k3 wkrtia 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 (whkw.*xf5l wkk3y?).    $kg \cdot m^2$

  A small 650-gram ball on tvq3njobu yg jy, +8wk*g h6rbzd/-o .0he end of a thin, light rod is rotated in a horizontal circ0 +8yvjdbg.uz/nr*3g-q o,wbh ky 6o jle of radius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl onj 5 vc/an3)l.d ie:btn a potter’s wheel rotating at constant angular speed (Fig. 8–42). The ijc/ad 5betn:n)3.v l 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 tp 0e:gq 7vdoa)he array of point objects shown in Fig. 8–43 a0qd:g ep7 )voabout
(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 consistsmzue(.dj4 48 .oismvr of two oxygen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning at the correct rf.hl-at) e;*l e.1abfa umy4date, engineerdefyf.a)m a ltb ; au.4-*hel1s 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 reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm and a mass of 0. oyf- hc, x:hur0rk*e(do:n-j6 ./pydqc*raq 580 kg. Calce /qh,adypr:x.f0ck r r-*cd-(onhj y:6u o* qulate
(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 fq1 gj0jwbo6an4v ksa409s9xto 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-) .qqfog) 5eiiyex+v;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 av)oge 5iyqef) ;q .x+ind has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is eventual 9l wj*piz0wf1bls 7b,ly brought uniformly to 7 lf09bz p*1, bwlswijrest by 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-kg ball and1m6v;g* r rbt 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action of the forearmx:slt ijavdb1ry4- q( qs,hb8 (3 tg.x, which rotates about the elbow joint under the act:xt314ls -(qjbgsyd(avhq r .i,8bxtion 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 Fig+ec6kl9 7lk9 3y*cmb8dcrtvr. 8–4 6ce+8ydlkcvlt9r37rkc9m*b6.
(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 masseqo5* 1lcd w29axg+opcouo 8t5 )rju;h s, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest within four full tuu(vdq / a *wv0n8k4mtprns (revolutions) and releases it 4pvkavu d/w(qtm 08*n 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 momf9xrpl ;tx1e5qy k7q/ ent 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,ur.uqp cf41n develops a torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls withov2eab.vu1sqc52ojt i5 vv+y/57 vuvs ut slipping down a lane at 3.uvs c2tyjvbqs1a5e2v/5vo 57vi + .uv 3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the sum *d/4x i5du) wgzizg0t of two x* utw/gz4z 0d idg)i5terms,
(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 u j s6v6kpp -vgidgd8*h v*:c1 vid5+k1640 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revoluch:*u1vv*pp-gdd5vjki +ig v 66d8s ktion per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1. +a::lclxii(;p0pw gr80 kg starts from rest and rolls without slipping:i( xglw+;c:p plr0ai down a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is balanced vertically on its tip. It starts to fall av+3q h:+xzd;xry e u57*hsjtond its lower end does not ; hzho+rdu7v:3yx*e +qtsj x5slip. 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 of a 0.210-kg ball rotating on the end of a thin siivh2d5ji94mosm:) 4 z 5t7le1jy cjok: 8dnltring in a circle of radius 1.10 m at an angular speed of 10jjc si dni hv::2e)j5zom5 9t17y484i mdl lok.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grinding wh.) onownaks9 x;on44heel of radius 18 cm when rotating at 1)nhan4 w9oo ;ox.s4 kn500 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 atw)1-fas l+k wj his side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal positiok1 l)ja-swfw +n, 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 moment of i+uvnhzqvy 6 8+(/w tbcnertia by a factor of about 3.5 when changing from the straightb6tqzywhu + v n+c8v/( 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 increas/m ezx hyi8s6 ;amk7b*e her spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a final rateh 7zy6*x /msibm ak;8e 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 tp3. co,9kl f1u vcuf4through 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 cm, onto the center of the rotating wheel. What is the fct k4,3lou9f .cuv1 fprequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular iz5ua8 sy6.4b+an ty kmomentum of 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 3d 4o uc0fukv5momentum 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 dropv1qvfp qr5xo,a3+b/ jped onto an identical disk rotating a vovpa1f5jb3/rx q+q,t angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns /6wdzm)14ex owxrtn,at 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 rotat z3tx4oz 2cp/fing merry-go-round platform of radius 3.0 m and c 23t/zfo4z pxmoment 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 ir-sfu gw9:qq ,ae;q)3pt1y svelocity of 0.su:fwts e) -y r319p q;q,qgai8 $rad/s$ 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 09f jcg4owu-ihalf its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would t -wu94 ogjc0fihe 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 invol em jza8i,i fgi .ifg4*uz8r8/ve 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 r. z:nja-o*w6l 4ii s)t9evk$ 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 rotadbzhd5b20x z9 te freely without friction. The moment of inertia of the person plus t0b 5z9xd zbd2hhe 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 a 6sk)q , )ctyn09scr *ik.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of inertia of 1700 k*) q ,0iktcsycr9s)n$kg \cdot m^2$ 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 o/ c z/gadlx)t7lk+/1)nwwwtend 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 the/l)dax+ w /t)1olwt7w gnz/ kc spool’s center of mass move?

  The Moon orbits the Earth suc t14i/wj2s p1ypgi 6vph that the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (abp yj 1 /2ig16wptvsi4pout 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 rest3n+f4d- kx-jhr4nrbj /0 jm3aaaha fh82m r *b 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 shaomrz/ubhlc679 5qu.e 4ki30hhovmg ; pe of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by t;e0moi7l9 h r4hvc mg6 hzquo53.uk/bhe motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical dit,f ijwn p)j25sks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concenjiw ft,2p 5j)ntric) 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-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 spevth7 vd6 *4ktenv*m 1ced of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 times as great, were rotatnjctv2,hdvx2 bhrw hi 29/7 *s35nqk hing 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 thatqdb ,s5v w 9j7hhn2trv2x2ch*3h kni/ 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 u 3e8- 6alkrtp 2tc8odm2lg7-fduqlj, se energy stored in a heavy 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 q-2cle 7a38trop26d8uk f gtml d-l,jflywheel “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 illustra z -qlec zlez5k(r w1 i+3x(fw(s5x9q)iv,sj ztes 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 sgivha**/ - fjrolling on a horizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (i.e., we ignorfjlf;6 3dwlt;5rd 34+m xlkfc wdcj9.e 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 them 45wdtl3k flj.fcw dl9c;rjx+63df; 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 t3n)b /.kduj7sjpr m-the floor, and we want to exert a horizontal force F at ij7bj k3tsdu r-pnm)./ ts 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 wt*p6 jjl+*spj ith speed v=4.2m/s on a flat road is making a turn with a radius The forces acting on the cyclist and cycle are thetj6*pj* lj+ps 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 af u+br9jo+u np39e a1f sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does tf 39eb 1nu++fo9jaurp he torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinh bxzw3d ;9qzy dth38esj s;134-vxzyder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular sp yb zzxyd;s3z e1vth3h4x9s3jd q -;8weeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a cnswyw wsc*dmm/1d-y+tfr.h -k 39w9 mlutch assembly which consists of two cylindrical plates, of msdscwwmm+dy1t- hw 9f m3r/wyn k9.-*ass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along the looped rough track of Fig. 8–5y 8d xasz0vmp 3t5ajkb:8x;hmt m .8:p8. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop without leaving the tra: 5xspka8pm dmh:3mba;t. 0jv8yx zt8ck? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do +,gze*.jmb(njktbcakx9 : 2hnot assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed uniformly frc5fb91rxbpx wni;9 ; gom 90km/h to 60km/h The tires px9;bfw59r icngx; 1bhave a diameter of 0.90 m. (a) What was the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s