12.43: Several forces act on a rigid body. If the resultant (nqw.o88pd7 b/i wj3 tpfet) force on the body is zero, which one of the following statements 7otw.88/qif3 p bwpjdmust be true?

  97.39: A cylinder free to to qt0*( kj:4 fmr;ru+pn2lwwn urnaround a fixed axis has a string wrapped around it as shown to thwpurqrk f;4:tm2 ln*(jno+w 0 e 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 j+ :.bptw9j)u jljz6 -,as4wxwomj(ecv81lyfixed to rotate about an axis through its center. The speajw ,m8j)w6.w (o: 149bzty -x lljvjucsj+tick starts from 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 rotatingtp l 1. *j yzroxx*g3yo6/v:t dkms:/i with constant angular velocity. When the angulartjk /:ioz y dx136*rlx*vpm /so :.ygt velocity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slippo9 *j5 . :fryfsmcekr:ing on a floor along 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 hasvmc3lzdj-jtmd 5q3e 8e u61h,z v3 ,ih mass m, radius 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 8 zq.7vr2wdou4iexum0s6da 3ew( x*esolid disk and an ideal uniform ring each have mass M and radius R. Each object begins purely rolling without ei7xw .2ux4v(zaoqdd30e r68m seu* wslipping 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 and an ideal une :lvisq0n3n id./ri8iform ring each have mass M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. The coefficients of friction for the disk anr: lniii q30d/e. sn8vd 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 cylindezkjgfup*iq 8p6+ o6ark v:)5u *urc8g r rolls without slipping on a rough inclined plane. Which one of the following choices best represents the tiv:f+uj 5urzc8 k6g 6g* q)or*pa8ukpype and direction of friction (if any) acting on the cylinder as it rolls up the incline?

  14.43: A long rod of lenx;b(fdg a wuh*ga;;w)gth L is pivoted about its left end. It is released from an angle θabove the horaw;( *h;f )ggbdxu w;aizontal. 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 rotate about a e9 ch1q-lzlp/ x-nn h60 db4tifrictionless 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 pivot. When the rod is horizontal, what is the magnitude of the tane1nxtc lh4n9- dz-ip bh6q/0lgential acceleration of its center of mass?

  16.50: A uniform stick of mass M and length L issbbef963w: q g m;fn: e 6rpl*f2et:ew fixed to rotate about a fricti*mb6 tepeq wf63erb:w fnlg;::es9f2onless pivot located L/3 from one end. The stick is released from rest incrementally 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 ofsue 35 dc+ywm1 three long uniform cylinders with equal radii on the end udw1y5 me c+s3of 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 aou6m7 e5-vmto4vvthi j /s(c3ndY, have masses $m_x$<$m_y$, 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 unif5xdm l/kx lv74orm disks of equal mass each are mounted to rotate about an axis fixed through thedvm/kl 7xlx54 center of the disk. Each disk is initially at rest. The radii of the disks are $r_1 < r_2$. 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,mw/yvv80ed;eez n,6 yd 7 e4azfb(f+p have equal masses M but different radii such thdzn ;y8d0 yff(pwm/+vv7 6b,4eaz eeeat $r_x< r_y$. 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 with a mass M and radius R is pulled by h 04j8o gtiqkbzfsv1 2)d;xc .a horizq84 x;20)tf.o v h1igzs bkcdjontal force F acting
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 mass M and radius R rotateqf,iig hq3-r3 s clockwise about its cqii3,ghr -3fqenter with 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=2.00 kg and radius R=10.0 cm is conteidgd-rhq6)7s, * l vnected about an axis through the center of the cylinder to a horizontal spring with spring constant 4.00 N/m. The cylinder is pulled back, stretching the sprin-t7)s*di rlqd,ge h6vg 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 sl .30fksr+uu:rmf9 fcjo5)*77wk aou dlam 2 kingle engine plane are turning in a clock wise direction with respect to the pilot. The gyroscopic action of the moving parts will cauru*faf+lucas 5:l)2u0o7dfmj 3mk9 ow7kk .r se the plane to move in which direction as the pilot tries to make a sharp lefthand turn.