12.43: Several forces act on a rigid body. If the re8 h1,:(oiu;aqwzkhpvhs+zb , (gb/bwsultant (net) force on the body is zero, which one of the following statements must be tp1,s /hug(hb wviq(z;zo8khw, b :ba+ rue?

  97.39: A cylinder free to turnaround a fixed au-5kd(3 zdopfmddikymuizd)/x 7+*4xis has a string wrapped around it 47 uzi-/+(md)xkp* mdi 5du3foddyz k as shown to the right. The string is pulled with a force F equal to the cylinders weight. What is the acceleration of the string?

  16.16: A uniform stick is fixn0l+recm 90rfed to rotate about an axis through its center. The stick starts frorc0n e0l9r m+fm rest and rotates through an angle of $90^{\circ}$in a time of 1.0s. If the angular acceleration of the stick is constant, what is the angular speed of the stick about its rotation axis after one full revolution?

  98.22: A rotating fan blade has kinetic energy K when r5zb:139ok 2wkjag shdotating with constant angular velocity. When the angular velbh a19zjk wsg3: 2ok5docity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slipping on a floor along +mngr.( cu 9x4ze 1j xqcgci4lmqc--) the $+x-axis$ (to the right). The rotational kinetic energy associated with the sphere about an axis of rotation through its center of mass along the $+z-axis$ (out of the plane of the page) is 20 Joules. What is the translational kinetic energy associated with the sphere?

  98.28: A solid disk has mass m, radiuse-h(h)hvymfu.;;f 4 1a zvxpc r, and rotational inertia $0.5mr^{2}$ . The disk is initially at rest. A constant force F acts tangential to the rim. What is the angular acceleration of the disk?

  13.39: An ideal uniform sa .t-nc9pfd6 aolid disk and an ideal uniform ring each have mass M and radius R. Each object begins purely rolling dcpafn6t- 9. awithout slipping down a rough inclined plane. The coefficients of friction for the disk and ring with the incline are $μ_disk> μ_ring$.
As each object rolls down the incline, which statement is correct about the force of friction from the incline on the objects?

  13.40:An ideal uniform solid disk x9n+a s:vnbij+*l:qri wd(7pand an ideal uniform ring each have mass M and radius R. r+n avd9nw(p *sj7i+ xli:bq:Each object begins purely rolling without slipping down a rough inclined plane. The coefficients of friction for the disk and ring with the incline are $μ_disk> μ_ring$.
As the objects roll, what is the ratio of the ring’s angular acceleration to the disk’s angular acceleration calculated about an axis perpendicular to the object’s face and through its center of mass?

  17.31: A solid cylinder rolls without slipping on a rough inclined plane.g 213ukf s1lta,z-wl s3mab *a Which one of the following choices best represents the type a- sw1tg uamz3a1* a32lbsf, lknd direction of friction (if any) acting on the cylinder as it rolls up the incline?

  14.43: A long rod of length L is pivote/ /c8wh (4y.z7hia41fevynmsr ; cmn ed about its left end. It is released from an angle θabove the horizontal1mec/cra;vmh 7 4w(finz y4.n8es/hy . What is the magnitude of the angular acceleration of the rod about the pivot when the rod is released?

  15.46: A uniform rod of mass M and length L is fixed to ro 3nh01yocove6 tate about a frictionless pivot located L/3 from one end. The rod is released from rest incrementally away from being perfectly vertical, resulting in the rod rotating clockwise about the pivon1ovheoc36 0yt. When the rod is horizontal, what is the magnitude of the tangential acceleration of its center of mass?

  16.50: A uniform stick of mass M and length.m 9,yl0 y1qfobwjp. m j3i)vx L is fixed to rotate about a frictionless pivot located L/3 from one end. The stick is released from rest increml9m.bm y3) 1xpiq,vjyoj .f0w entally away from being perfectly vertical, resulting in the stick rotating clockwise about its pivot. When the stick is horizontal, what is the tangential speed of the center of mass about the pivot?

  06.24: A person tries to balance vertically each of threqd fon-jmrg)7oe 0f.) i 8vs:fe long uniform cylinders wi g-ms ))jfq8:vodiff 7.o0re nth equal radii on the end of his finger:
• A wood cylinder of mass m and length L with moment of inertia I
• A bamboo cylinder of mass m and length 3L with moment of inertia 9I
• A concrete cylinder of mass 4m and length 2L with moment of inertia 16I Which object is the easiest to balance and why?

  14.39: Two uniform disks,X andY, have m0)bsdrmk( t m,8 kk/6ppnaw5 uasses $m_x$<$m_y$, equal radii, and equal initial non- zero kinetic energies. Each disk rotates counterclockwise in the plane of the page about a fixed frictionless axis through its center. As shown in the figure, a force F is applied tangent to each disk at its right edge for the same amount of time. After the forces are applied, let L represent the magnitude of the angular momentum about the center of a disk and K represent the kinetic energy of a disk. Which one of the following choices correctly compares these quantities for disk X anddisk Y?

  04.46: Two solid uniform disks oqoe( fbp dd ln*;k8*2vf equal mass each are mounted to rotate about an axis fixed through the center of the disk. Each disk is initially at rest. The radii of the disks aro;8bq(nel f*d2d*vpk e $r_1 < r_2$. A force F is applied to each disk at its edge for the same amount of time. Assume that friction is negligible. What statement is true about the kinetic energy K and magnitude of angular momentum L of the disks?

  15.35: Two uniform disks, X and Y, have equal masses M but different raf cu oavya*:+0dii such thy cvo0a +ua*f:at $r_x< r_y$. Both disks initially are at rest. A force F is applied tangent to each disk at its right edge for the same amount of time. As a result, each disk rotates counterclockwise in the plane of the page about a fixed frictionless axis through its center. Which one of the following choices correctly compares the magnitudes of angular momentum L about the center axis and total kinetic energy K of disk X and disk Y?

  10.40: A uniform, solid cylinder wit)nsp v4btrooty*yn*8 nq9xwe;o63 q* h a mass M and radius R is pulled by a horizontal force F acti o*bnywq*468onver 3p )*;oxqystt9n ng
through the center as shown. The cylinder rolls to the right without slipping. What is the magnitude of the force of friction between the cylinder and the ground?

  14.49: A solid, uniform disk of qp5co- z- xxcl.b h-x5;fsj ocwwqw4(655tm k mass M and radius R rotates clockwise about its center w5t6x o- wlso-w; f5cz hqq-jmcxpw54b(k5c x.ith an angular speed $ω_0$ . The disk then is placed onto a horizontal surface and begins moving only to the right, slipping as it rolls. The coefficient of friction between the floor and the disk is μ and the
frictional force is considered constant throughout the motion. What is the angular speed of the disk when the disk starts rolling without slipping?

  09.40: A uniform solid cylinder of mass M=2.yd )ck+d81dzd6x lz. b00 kg and radius R=10.0 cm is connected about an axis through the cen c.x+zkddd8b61)z ydlter of the cylinder to a horizontal spring with spring constant 4.00 N/m. The cylinder is pulled back, stretching the spring 1.00 m from equilibrium. When released, the cylinder rolls without slipping. What is the speed of the center of the cylinder when it returns to equilibrium?

  01.39: Suppose the engine and propeller of a single engine plane are turnijw94pe,,*8 9zhbh;gf z czb h9lhsj*o ng in a clock wise direction with respect to the pilot. The gyroscopic action of the moving parts will cause the plane to move in which direction as the pilot tries to make a hjb,49zc*bw8efp z9oh9 s, l;*jhhzg sharp lefthand turn.