A bicycle odometer (which measures distance traveled) is attached near the w6 mslz8uv0mzmhn7j vwv. 0sk,i9 c)+yheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle witm8 jm,hvc y.067nv)0l usk 9is+ mvzzwh 24-inch wheels?

Suppose a disk rotates at cotqg*w6qz9o f 7nstant angular velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial an6g*zof q q7wt9d/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a singl+fqtd z-+5pe 7gmfnp)jz:: ** ogprnae value of the angular velocity $\omega$ Explain.

Can a small force ever eh*g (ial ihzm ,f50wt9w8y 07obu(gzs 5-q xemxert a greater 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-upmrjwez6es b5c5 953jnmxyx7 - with your hands behind your head than when yo7xm jnmz55jyrcsw 5b9e3 -x e6ur arms are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at-f 0p4hkckflbx :5ly/ the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it b p- kcl0:klfy/x5h f4harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower legs with fles.wk,y8iici oonc t( .y;ys6u1h and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distributionsciw( c,n.yyi6;18kutiyo o. of mass is advantageous.

Why do tightrope walkers (Fig. 8–3r(dap.dk, 8atmajwy,zz) 2r 6 5) carry a long, narrow beam?

If the net force on a syste4, g -fzlklp-ayssy)i5:2p ufm is zero, is the net torque also zero? If the net torque on a system is zero, is the net force zero?ig --afspylks 5 ),uyfp2l4 z:

Two inclines have the same height bur49f nimbegn6 k 38fj3t make different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be g3bmi 43 kn rnfgjef698reater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an incl0zq+yg lb. wk)i/0ny sine. 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? Whi+yzy blqg s.kinw )/00ch has the greater total kinetic energy at the bottom?

A sphere and a cylin2 qpo (tmpnm83qm7 b;r 7t5qw3exck::zeqo 5vder 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 3 xq7 ; kpm5v:mqz(n2rbcwmt 5e op8 tq37eoq:greater rotational KE?

We claim that momentum and angular momentum are conse+af /g .oqlt(1a rtv0mrved. Yet most moving or rotating objects eventually slow d/( m1+ql atf0ogavr.town and stop. Explain.

If there were a great migration of people towuq+5ez2i9edkrc9v p/g : k3 ym3xnr0zard the Earth’s equator, how would this affect the length ofcx rg:kpm zdr+ e99nk23uv ei05qy3/z the day?

Can the diver of Fig. 8–29 do a someevh*yh:r q2c*rsault without having any initial rotation when yceq h**rhv2:she leaves the board?

The moment of inertia of a rog tz9pbhr;: op x1-ff04vy;jqtating solid disk about an axis through its center of py; rqgozfb-tv04 ;:p hf19j xmass is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holding a 2-kg mass in 8dpb8ew7v(lc each outstretched hand. Icd8w78p ( lbevf you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identirnp y3) jnl4:tcal and have the same mass. However, one is hollow and the other is solid. Describe an experiment to determine whicrnt:njy p4)l 3h is which.

The angular velocity of gner s qo0cm17gp6w9;a wheel 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 acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasingc;s0 p6mnr79og 1w egq?

Suppose you are standing on th ++xgy;;u hbhnqw+ 1axe edge of a large freely rotating turntable. What happens if you walk w+x++huy ;a1bnhqx;gtoward the center?

A shortstop may leap into the air to catch a m)kywum,j s ,c 1r6x)sball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you lo,sxw kjmrm1)c ,6su)y ok quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discuss why a heliyo pkcp::21 kpcopter must have more than one rotor (or propeller). 1 :pckkop:2 ypDiscuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angle u478se(ich/ze5vw jn s in 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 Earthfqwv x:esu7mxk3+ -nwl 6 9v,w because of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the f6v ,: k+xwe93-mx 7svn qwuwlMoon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The bea *.zli , dwox8kxj19jdm diverges at an angll,jd8kxxwi9 j d o.z1*e $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender roxa,hf-a zz9e mrq (ar 8.(pog1tate at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleratioazq9 zg.hm-(ra xfr8 ,apo1 e(n as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 w;3 /kcc5go mmanr8k 2m to another child. If the ball makes 15.0 revolutions, what c/o 8 mgn m;35ar2wkckis its diameter?    m

  A bicycle with tires 68 cm in diameter tra .b p ls/msz-ymg0diirztr4:rf8 1)g0vels 8.0 km. How many revolutions do the wheelz4zr1ys -p08s)bgm:.lt f g/midr i0 rs make?    $rev$

  (a) A grinding wheel 0.35 m ,n2za7b5(ndsf gbu :vin diameter rotates at 2500 rpm. Calculate its angular velofsgb7 :u(dbzav52n ,n city 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 complete3d uo tn0 dwyt*5jzmo;+k9a )j revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seatez3j omw0n)a+5ytudokjd t;9 *d 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in its orbiy )u/ lev+q2l;,*jyh bvrwc *iq52mg qt around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed0thn(ndja5u0 tmv; 3v 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 rotat df:ngo83 b/ynw)9qb ce if a particle 7.0 cm from the axis of rotd og3):8n /wn9b bqcfyation is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelkpxl6j78 8;qknul- /qzai0jcq)( i emerates uniformly about its center from 130 rpm to 280 rpm in 4.0 s. /p ik8celk x6i0(nqq7- zjq)jla;u 8mDetermine
(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 radiuslu p z(g2m(w.g $R_1$ 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 Apollj1a kp,jgm7i f5 s//sdpby,h5*aace. o spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start gmcfp 5,iss7p /*y a5ade/hk.j, ba1jof 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 kk0tmi3( z*45cm t sw,wmu/dquniformly from rest to 15,000 rpm in 220 s. Through how many revolutions did it turn in this t(0wu z5tkcim*3 /msw d4 k,tmqime?    $rev$

  An automobile engine slowsaed2aga y x*4w,hw+m: ld.sp* down 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 stj(t ;bd/nh.b qresses of flying highspeed jets in a whirling “human centrifuge ; hqb.dtbn/(j,” which takes 1.0 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 rp1r,w 5wibnvna7n*q h8 +amne+m to 360 rpm in 6.5 s. How far will a point on te+8nr ,nn wai7b wamq+h*v1n 5he 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 150 p m6km2z /9aq:g0-meg ofjy9q0 revolmyaq /of62qeg9g :mmz 9 kpj0-utions before it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car makev-d3x:)n hnoo 5o6cdl 65 revolutions as the car reduces its speed uniformly from 95km/h toncod)l-ho 53:o n 6dxv 45km/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

  The tires of a car make 65 revolutions as the car redun,sllt(9q*v x ces its speed uniformly from 95km/h to 45km/h The tires have a ds ,l(*9vxnt qliameter 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 c6 qa* (u2 jiuh,uc)skher weight on each pedal when climbing a hill. The pedals rotate in a circle of radius 17 cm. jkua,(shc*)6ui q2cu
(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 c(6qsfg8x,pp 7a*u yp74 cm wide. What is the magnitude of the torque if the force is*7uypq 6 (fx,ac8pg ps exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wh x19dzv su/1mteel shown in Fig. 8–39. Assume that a friction torqueudzm9s vt1 /x1 of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are a4 +c)hjl+b 9ibwgj p;jttached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the b4cg+pj;9bjw+i l )h jmagnitude and direction of the net torque on this system.

  The bolts on the cylinder hgnb9:d,oao:ci z 4dkn: yci0*e. *vrhead of an engine require tightening to a torque of 38*v z c0ndgrinoabc:9ie:4:,* o kdh.y $m \cdot N$ 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*8/dyy rq.n zw a 10.8-kg sphere of radius 0.648 m when the axis odzq/yr 8n*.ywf rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. The7u )ynwjfz a- qlxqy-o20 +ln- rim and tire have a combined mass of 1.25 kg. The mass of the hub yn7a wu -)jyl+q-lxzfq -no20can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod inck9l m* g(yh e*a vx*.k+ana-s rotated in a horizontal circg+ akel **(naah*-xn c vymk.9le 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 bog3puap v, .li;wl on a potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and the clay is 1.5 N total. ui3,l.gp ;vp a
(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 8x l3snkn 5:fo 0+owbfinertia of the array of point objects shown in Fig. 8–43 axf 0so f+wb 5nln83o:kbout
(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 * anl b7dkk34 z r05g,ff7*fijg aje:atwo 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 ly;39*mmgd47r2cahb p4bua g satellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg hru 4y9glg* mc amad7b23;b 4pand 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 ge3x u r84)x3dz9f;fcfuf /wg and a mass of 0.580 kg. Calculate fg 9 )dz3 fxgu4fcru/3wx8f;e
(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 i/go hs2l69 cer a)nhx .kayk/6t from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-driven merry-go-round andwac j12:bdi2 k 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, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleratioib2j2k wdc:1 an, 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 brru g9rl5 g0w2lought uniformly to rest by a frictional torque oul2gr l5wg 9r0f 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 a7 ywahc qjd74nm2* x wdz6pla9d,u; j* 3.6-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 4rqh/uuhg 00p2 r-wbh,hxo3l ball is thrown solely by the action of the forearm, which rotates about the elbow joint under thelhp w, h3rr bh0hq0u-o/xgu42 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 showjlmqu 7 4dg29r0 vwod.n in Fig. 8–46g4ddo.wl 9v2 qjm70ur.
(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 yaj..sezl;9 ) , 9a3evjxto 9znsuo6utwo 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 5e)+9 idi csy dqgq. q1v:t 3xwzfmh+:hammer from rest within four full turns (revolution1i fqeg: c+wx5s m .+)dvqdy93h:tziqs) and releases it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of inermvl g 1)xd2w3ytia 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 285o1 r8hkt 4c;scbh5 fx0 $m \cdot N$ 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 mms +a, hgf nvlc6*c9)without slipping down a lane at 3.c)+,fmmcnhg6 lavs* 9 3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy 9b-4)k*qpfp1y sep.eekv )c mof the Earth with respect to the Sun as the sum of two tepem pye 4kfq) eb1cs9-pv.)*krms,
(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;;k -lq q,fqch 1640 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotationqhlcqk;q ,;-f rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts frop5s,tklo (6s em rest and rolls without slipping e,l(o 6psk5s tdown 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 x 9w*4m2mwldj1 1htnhfall and its lower end does not slip. What will be the speed of the upper end of the pole n lm whx dm1t29jw14*hjust 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 thm)s,,i9 u yogtin string in a circle of radius 1.10 m at s) ,,tgi9mu yoan angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grinding wheel dxi etg6xi)r2 v):5viof radius 18 cm when rotating at 1500dg v):e)ixx i6tr52i v 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 pobg3 dc k d5zh/qa30x0u+ecgu,i;,zglatform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decreai uch3d0/,u; c3,gzoqgxdb+ k5 0e agzses 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. 8–29mpob:9+47zrq b:os fb) can reduce her moment of inertia by a factor of abou:rpbzmo 7sb 4+qbo9f: t 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial rate of 1.0 3bwvr7y.3a mv ,kux*qb1mla;rev every 2.0 s to a final rate of 3 * l ,.;vmxvwa 33ka17mbuqybr $rev/s$ 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 itl0ezc ,g7.f.2dp yqc rs 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 d, c7g. y.el2rcp fz0qof 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 o)lx v0dl9wo/)3k h ceg;fc ju6f 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 momentum of the Eartkhhq 30.xc.dr h
(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 inertip z (1-dv/la6u usgyd5a I is dropped onto an identical disk rotating at angular speedyg uu61dl 5-a(dpvz /s $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.42 7iq+ utq8p2j*pai(e skv bq/oa9 9id $rev/s$ 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 merry-go-round platf 7e15. ofu+pm 6yakvy h9exgj4orm of vyy7x 9+ pj.u k5af1oeh6mge 4radius 3.0 m and moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely with an47bqj54ho *ji:u: +n qejet 5puuwop : angular velocity of 0.8 :*pp:4qqnu w5b eijej+ouohu5 t4:7 j $rad/s$ 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 whzmp 2) o dcdq8) j3/o-hs*+fc.qzuhj dite dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass car qqdc+/ozc3zp)uj.) h8*df m-h dojs2ries 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 )uflfed );zq7 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 grs7prz s/8,3 hqgf)x91njpi $ 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 rest7b85 cb/locp r, that can rotate freely without friction. The moment of inertia of8 5ccr/o b7pbl 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 a 6.5-m diameter merry-go-roundskf pyoef *;+; hj mk-c6y.l.z turntable that is mounted on frictionless bearings and has a moment of inertia of.- ;e sk+y kh.jc 6mf;pyolfz* 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 afhprbgm/)pte6c.k wp1.,k/ 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 spb1/p e mkhf/k)p pg 6.rc.wta,ool? How far does the spool’s center of mass move?

  The Moon orbits the Efixgyk d-8 am./bvf5/ arth such that 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. (Inia -d/mg . 5fvfk8bx/y the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from xi3whi br 1/c1u;zp9vrest 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 of a uniform cylinder of l;di4) m ofzpx8bdl( /d9qq* cradius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular accelerationp(b doz 89d*x4md q ;l)liq/cf. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of massvsr/z 6 +5p0l g p*jznzwq*jq0 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of jgn*z+j0qw zpz5r6/v *sq0pl 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 speedy)djjgq mux le.mu(/x5s-f41m r + ym, 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, we *lv9k-oih r)0uuvc o-qkc+7 dre 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 star okk lvuh7cu*dq09-v ir+o)-c 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.yai i)wui 0m8 for it to use 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 1.5.mwi8 ui) i0ya0 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 gth,p7w6d a)7 in(iovan $H_2O$ 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 surfa9y mj+ i1wg 5itl-ldh 7qcep-)ce 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 M0hla0x13eq ip* y;ymm and length L can 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 the rod, as shown. [Hintq x3ei; 1*a0yplmyh0 m: See Fig. 8–21g.]

A wheel of mass M has radius ;ky2v 3tdrbka,d0 / n8ycvz 8ckf(h l3udv-6hR. It is standing vertically on the floor, and we want to exert a horizontal force F at its axle sc d(y-dnv 0;d8 k8uyf6vch3, tahrz2b k3l/vk o that it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road islq( )kbey3 s 3iaet6o) making a turn with a radius The forces acting on the cyclislsiq(oeat)6y)3 3 ke bt 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 of length 1.5 m and begi h9ym f7pz3 sd-3)byuans 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 thisp syy-zb h3mf)ud7a 93 feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinde;3pq vpugp*ii:/k+d i r and her arms as thin rods, making reasonable estimatepiq :pk3+p i *gv;/udis 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 assembly which consists of two w9fc.shth ct9 *.r,z-kp js6xcylindrical plates, of masshsk w*6 ,z.9s.hcj pt9fc- rxt $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 roucdtg7)lbn k+ .9tzph2gh 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 high79t pc +lt)d.znb2 gkhest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not a - s7cadlrjo98-zqzv .ssume $r\ll R$ h =    (R-r)

  The tires of a car make 852 +:nz9nst wx8kvqv kt*t9n9 s revolutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diametevn wx2qkk:sn*zt989 9tvt +n sr 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