A bicycle odometer (which measures distance traveled) is attov4*q+zw3:so6j1o9lx yhn w yached near the wheel hub and is designed for 27-inch wheels. What happe6vy *yh1oqo3w4 +sx l n:jzo9wns if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. D*r(u f8h5g i7sil odj6oes a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acces*ig875loi(hf6 jud r leration change?

Could a nonrigid body be described by a single value of the angular velocitytg h*on:s3yx 2zst0/y $\omega$ Explain.

Can a small force ever exert a greatj3w 4j09ub cveer 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 difficultltd70gucgo /w l9k;0t to do a sit-up with your hands behind your head than when your arms are stretched out ikt0l lwg 0/7 ;td9ocugn front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockee2msx jeg 2kbs2 )7(ngts at 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 hardj7egxs2n )bse2 mg2( ker 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 fleshz;u1,l p f4ywkw5 r -c+io9r *dfwbf;p and muscle concentrated high, close to the ,5wwd4pfz- *cu9 ol1ybf;kfrwri;+pbody (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, narm1 viqsz/r(*f+ j-eimrow beam?

If the net force on a sysdt70/rw - ukk2jl: qkztem is zero, is the net torque also zero? If the net torqd/k0ul kw-kz7 2trqj:ue on a system is zero, is the net force zero?

Two inclines have the same height but make different qp)ehkb*0nd c; u::b yangles with the horizontal. The sabu:y )ned;pk:0b qhc*me steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start r9x)0px h:a+a2nr; k5 cjy qrwoolling (from rest) down an incline. 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 thernx awjx5hk)rp2q;r:9 coa0y+ e? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They stm:jov 3;u x3dyart 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 jom3yvx 3d;u: energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angv .r-p11ows6oelsc ;jular momentum are conserved. Yet most moving or rotating objects eventually sl;e swr-o1o pls1v.6cjow down and stop. Explain.

If there were a great migration of people toward the Earth’s equatbgf 8 6u5(lcmzvli +l5or, how would this affect the length of the day(bvl ufcz55lgl 6 m8i+?

Can the diver of Figyn d7v6 i b9q)qz3 .frpjiejy4.w4x8h. 8–29 do a somersault without having any initial rotation when she leaves the boarf6erj dq )97by4jiw4vziqpy h.. n8x3d?

The moment of inertia of a rotating solid diskx 2u7erex 88alv/o4hj about an axis through its center of7 hj8r4u8xl2x ee v/oa mass is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holding a 2-kg mass in each outstrehvyn v1hxu*ced s 8-f +-/(ury:i+k kdtch1dnr +x8uhuidhf cy/+kv-: -ek *v s(yed hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and havewvd sij-l: m jys3 5yoto)6c(8 the same mass. However, one is hollow and the other is solid. Describe an experiment to determine whiomt3ydw)oy c8( 5lv:6si-js j ch is which.

The angular velocity of a wheel rotating on a horizontal axle points wesi xnh;y7nwn)m1v- / :alsm ;hlt. In what direction is the linear velocity of a point on :yhnxvi wsl7-/n;l; mm)1 nah 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 decreasing?

Suppose you are standing on the edge of a large freely rotating turntab3bf/ ip w(v42dmzjow .le. What happens if vw( f3/ .pj4w zb2iodmyou walk toward the center?

A shortstop may leap into the air to catch a ball and throw it quidcz- 4jpi;e d7as1,i,z jzsn- ckly. As he throws the ball, the upper part of his body rotates. If you look quickly you will noticia-c,eizsnzpjd,z-7s; d41j e 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, discusskl 1w iauq9bi(ctj 5;2 why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second prope5i c(bqt9aluj k;i12w ller can operate to keep the helicopter stable.

  Express the following angles in radians: (a9yht 609pzhvq2beh*8v t 5kmy ) 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 Eap/so)k tc zh5s7uo0 9jrth because of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diksth/u o790)pcz5 ojsameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam mh( *s60ru-2)h n lswp. z ne(9mcgwctdiverges at an lsgh9z emn(wp rn s.ccmt6-(u)02w *hangle $\theta$ (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 x. /-lwp*bx zyof 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 xzx lwb/.py-*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 therui4; 6arq r)t ball makes 15.0 revolutions, what is its diame )4qr;ir urta6ter?    m

  A bicycle with tires 68 cm in diameter tra * q .f/5khna) s-niy,qvwbj-/v;o gazvels 8.0 km. How many revolutions do the v h)yni*5aa,q-o/.z;sk/v qgfb j- wnwheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calcu g1nq0.mya ,rwuui6lq0y45ib late its angular velocib 4m,0 .5 ygqa6nir1wuy ui0lqty 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 chc 3h(5 r e8uk8/ythlfomplete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 8fh/lrt(k85uy3eh ch 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 v;lw7, pr*z+j.sq sz koelocity of the Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear spb5nsxwy5 i4f: eed 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 r(b2+,0y:z *d q umwmwy7ebju jotate if a particle 7.0 cm from the axis of rotation is to experience an acceleration of 0umd:jq * yej,m(wby7wb2u+ z100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel acceleratesv4rab23 ig hg1 uniformly about its center from 130 rpm to 280 rpm in 4.0 arbiggv3 1h 42s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radiu, jkiptae35tn:w)4 cb 2e c7kx ;m3ions $R_1$ 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, astron)azp,n7 ac9/ogevx/.dwdfr 0auts aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s enzep7f.cr)0gxndw/oad ,9v a /ergy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm-q0o9 t 0e9s z psxs;oylj;h f:k/o pxz*,ub.r in 220 s. Through how many revolutions do;zxz9fkpxost,ysro p*;0.ush:e-j/ 9 q0 blid it turn in this time?    $rev$

  An automobile engine slows down from 4500x ).l) uschzs9 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 flyingq3 jzz/p 5:mju highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete rezm3z: 5 /ujjpqvolutions 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 /,wk xr8r-xor4v , o(y 5pvrurfrom 240 rpm to 360 rpm in 6.5 s. How faoyr, 4rk5ox -rvx,pw (urr v8/r will a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is r 6mo2kjf ybq2csw8)s 4unning at 850rev/min It turns 1500 revolutions bejsb 6c s2 8yomfk)4q2wfore it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the carsif,wm) + dfv9h g;wr,;oq d 9(hienk) reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.80hmww k(fq,hs;+, )i9 odigd efv rn);9 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 rm-k p/s0av us.educes its speed uniformly from 95km/h to-kuv0. /sma ps 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

  A 55-kg person riding a bike putb+nfv h49 +2wh, fokins all her weight on each pedal when climbing a hill. The pedals rotate in a circlehno,++9kv n f bfw42hi of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74o x t,g0gil7i/)yu ct6 cm wide. What is the magnitude of the torque if the force is exert6u/ g7) ,goi0yi tltcxed
(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 toro 4b6zj y0/ifjl l(ru wt4:kl3que about the axle of the wheel shown in Fig. 8–39. Assume that a fl ujb ll:(f30wo k6jt y/r44izriction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of masfry3k s)egm.rsw; *vag72 kr6oy;1 z ys m, are attached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal posie3 aovykym;s 7;2rr )1rwfkzyg6. *gs tion and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an enz*8 j9bxc) zyvgine require tightening to a torque of 38*c)yzz vb j89x $m \cdot N$ 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 10xfc4ni7k q8f :dop2l/.8-kg sphere of radius 0.648 m when the axis of rofl4ikdpncx7 2:f8/ q otation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a 2o3jt+vy y19ch)t gg :i8ynm4peo hi6bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass o y1ptvg3 )6cet:gho im+2 oy4n9yhij8f the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod ivyyvw: uns,qioh,( e;w)0 j x4s rotated in a horizontal circle of radius 1.2; ieo0uvwh4, qxyny( w,:js v) 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 on a potter’s wheel rotatin0d9yyhq; ff evpg7jv9nr 3.i6 g at constant angular speed (Fig. 8–hfjy3nfp ;9eg y vvqir670.9d42). 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 point objects showf5t 5di/lg8hng w )/icn in Fig. 8–43 abouf5tdw/ih5lc/) i g 8gnt
(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 two0b r84sez3bx((:uicwt omp*k 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 tns t)(a jfnk 779nplv9he 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 rocketsnn97f n9pt7vl ak()j 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 rl8/ut- l of:aand a mass of 0.580 kg. Calcu8/ulo:f tra l-late
(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, accelerap(mmh/c pyszwu28+c 4 ting it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-d0-m+en g-g9ewggn cxyq 35 0w:ngym*oriven 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 isc:nggmegg0 w e gw3nn-*+ ymyoq5-09x 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 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 ot/5f(u: u+v-hz-wzlm hfyh g8ff and is eventually brought uniformly to rest by a frictional torque o+t-uzy h h8lf (h-gvwfuz:/5 mf 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 accelerat,te.s230ynyy.j f hhces a 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 ball is thrown solely by the action of the fo ge7+3s z n) p2k2nqokxs*xkh;rearm, which rotates anx72zgqs; k3 ok+*2spnk hxe)bout the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thin 5f3mketdr1 x wv4 d a7e10-bfwymc 6y0rod, as shown in Fig. 8–465ew70tw-kyd1vf f60e m y4r a3mdxcb1 .
(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 twhwrs i/1v7k- kqva;sl02q -bj o masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest within four full turns (r48sg2mdoiq aa m2- .dmv9t2dpevolutions)vpd -goa98a.2dm 4s2 qm mit2d 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 momyxl na+;wi9 :za34emabci,q, 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 develops a torqu9nx;c x7x qq i.8f5aaw m2d8eme 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 c.b81 iims f*0obrqq w;5eb4fand radius 9.0 cm rolls without slipping down a lane at ;m.f*158cbboi4i0fwb rq s qe3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respe*9:hiwp i, :ugajyf4nrjv r4z2cl.i(ct to the Sun as the sum of twch(2.g :v i z9ajr* :jui4lipnrf,y4wo terms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.50 m. Hrvj/wn4z )bu ,ow much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution ,r z /jnubwv4)per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rw3mzwx,n5s,z;5abc z est and rolls without slippingzbm5cznz3,5x;wa , ws 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. r;uc t tff9ft51 r3jg0It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just beforecf3 ujgttft19f r;r50 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 enzdq fwb+zz*r -v ,kft6lnp),*d of a thin string zf+zqfk n,)*-r zw ,tld b*6vpin a circle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grin q4nh,a.0c mxnfkiet *) f9z9ading wheel of radius 9xan0mk,.9 zaceh )ft ifq*4n 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 znk j1heztr;t7dsyz4w: xyv 5e..d- 0 a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal positke5jxh-trn4vd zwe7sz ytd:z .;1.y0ion, 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 rn n i*axogt3/,93 fc*0lmcsx her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.33xiraxcs/o 9cf *n,gtml0* n0 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 ra-ukowr+5k r f4te of 1.0 rev every 2.0 s to a final rat + 4kuof5w-krre 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 ceruoc*;er*y ij r i.x/5nter 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-k.jx r ruc;re5y /o*ii*g chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinninym4 kp,j7gp4)iz1wszg 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 );ftar.l p :bslw34 xgmomentum 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 d0 f7o6 lgy eqyk-:*eimoment of inertia I is dropped onto an identical disk rotating at angular speed ldy o-g7kqey06:i*e f$\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2u 3 lv3eaf4;da.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 stad( 6*n; ep q*4kj*o2mp/wnzldex vq)rnds at the center of a rotating merry-go-round platform of radius 3.0 m and moment ofjmz)v2 pqo*k e*(dn/ 6x;*dqnwl 4rp e 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 rotatibr ;pb;kr.nb p-z7(pw ng freely with an angular velocity of 0.8p-pz.; b b7prr; nwbk( $rad/s$ 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 iur50ujlyze 8 -7uzc y5nto a white dwarf, losing about half its mass in the process, and winding up with a radius 1.e8z75u cuy -zy5ruj l00% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve win xt(8mjs (yqca )l6oj:ds 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 e14rb0s;z aes$ 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, ininp s:dln4l9crxp3 0f5pw76b atially at rest, that can rotate freely without friction. The moment of inertia of the person plus thpds7:lpn r30lxa9 w5cn6 p4b fe 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 ,quqaxoa*88 r 3v)z cothe edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless3uxqa8, )*coazqo 8r v bearings 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 w qs fw5wfi;a9n.nl4+lbt 27 nwith the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? H ns4w5nf2w +fll qa;9bw.ti7now far does the spool’s center of mass move?

  The Moon orbits the Earth such that thq, j+mnwsz/e .a iw3m(e same side always faces the Earth. Determine the ratiow3qa/ j,(zis +.nemw m of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from fhjr--uk7nw 6rest 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 cylinder00 ye xs(l+eyg of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s iny+ 0(syle0ge xterval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of 7lx-- 0r du4rge5c: twhk;caatwo solid cylindrical disks, each 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-long7ek w5-uarg d4xcl :0rhtca;- string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how i1vr rnz/.4f 2qnn9ww9b-zq xgs 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 Sun, but witiipp7l7xy0abfvx- :cwe+kg f 9:d- 2oh 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 star is a uniform sphere at all times, and that thex-fe pa bg:9v- 7 i7cy0ix2l +dfpk:wo lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use energb4,t c oa/mk+t-b*mpyy 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 flywheel +4 k/-t,boa cbmp*mty “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 lz78 u-:e)3 cxwgu oen$H_2O$ 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 ai.k*cug/ u9z z8fiv- :k/ vnint 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 pivozar ei r-cd.tit3 bfkz5u 40.r+*hw(tt 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) ttib5t3 r4r0.a ec hwi-* tru. (+fzkdzhe angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It-h7g/:m4 3zv8potyl zdevph . is standing vertically on the floor, and we want to exert a horizontal force F at its axle so that i -/zy g748phvmop3z:he ldv t.t will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist travelin+a ozdv 7b8c1fvtt(j 7) 4jacog with speed v=4.2m/s on a flat road is making a turn with a radius The forcttc)1dv7v4j8ao+jcaf b7z o( es 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 of length 1gox4tjvo2 -.,2adqd f .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 2g- ao.t qd,2f jovx4dtorque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thin rods,z)+hru 0wm0kj7f wp.d making reasonable 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 bomdf0z 7hujrw ) kw0p.+dy.   

  You are designing a cluan0: jxw *tacy*q h(7l2u4pkh tch assembly which consists of two cylindrical plates, ofapq(hltj yx0 h*n7c ak2u:* w4 mass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along the hwkr*kqb k95 8looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop without leaving thek rh895kw*qbk track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but d*g jw/w 9l4 ysyaau:x sk03r)po not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolq12v0 tzk.opkd8v)h z utions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of eao2kdtkqp.v 01z z)8 hvch 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