12.43: Several forces act on a rigid body. If the resultant (net) fh.)n5hh hl ,nqu2 sp-(xlf(dq orce on the body is zero, which one of the following statements h) h5q(nhhs u,nl-xq2pd(.l fmust be true?

  97.39: A cylinder free to tura):r ,yaz,vni naround a fixed axis has a string wrapped around it as shown to the right. The string is pulled with a fa: vy),,zanri orce F equal to the cylinders weight. What is the acceleration of the string?

  16.16: A uniform stick is fixed to rotate about an axis throughmkzvaat j*2,*c a d5q8 its center. The stick starts from rest and rotates tzd*j 58c am,* 2katavqhrough 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 rotating with consi;cc :hh)qx r1wk8 p1ntant angular velocity. When the angular velocity is reduced to one-third, the kinetic energy beck:h1c ;8h)q1 xrcpni womes

  12.33: A solid, uniform sphere rolls without slipping on a a wp 3k ks1bgut7 84cjkc-,xg5floor 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 has mass m, radius r, and rotationals05pyj4p.z hngxyf q;, .iq+t 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 solid disl- 2-tyhjc*h yk and an ideal uniform ring each have mass M and radius R. Each object begy-2cthj-h* y lins 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 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 uniform ring each have masih9/rd :r*(0zy z 0qf rcrwi)iaei .;js M and radius R. Each object begins purely rolling without slipping down fr:0;zd9iwcrryzeh0a /ii ).*j( r iqa 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 roughvi:wu an7mqn bdu8* *o;h*9id inclined plane. Which one of the following choices best represents the type and direction of frictiw;*h n98bi*u vqudm7o *an:idon (if any) acting on the cylinder as it rolls up the incline?

  14.43: A long rod of length L is pivoted about its left end. It is k-ug72 *-fr0n2mo-j5 vl f vftv zdw:zr1kn,oreleased from an angle θabove the horizontal. What is the magnitude of the angular acceleration of wm2rfz0:5 vvu-f zn-- tjl gr2vkkof*1 7n,d othe rod about the pivot when the rod is released?

  15.46: A uniform rod of mass M and length L is fixed to roj b4seabk8 chvly3++5tate about a frictionless pivot located L/3 from one end. The rod is released from rest incrementally away froma5 yvhsb+ +8c4jbl 3ek being perfectly vertical, resulting in the rod rotating clockwise about the pivot. When the rod is horizontal, what is the magnitude of the tangential acceleration of its center of mass?

  16.50: A uniform stick of mas-o5rdb/j tyz 9yjm: 7cs M and length L is fixed to rotate about a frictio:djj- ortcz59 m b/7yynless 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 tmu3t; xjc(e 1h*yxxmfw* (swx 4 0z*i3mxmhk.o balance vertically each of three long uniform cylinders with equal radii on the*imwezxxx 0mmfwh*(j13*xs t c.yhm;4 k3xu ( 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 an6ssezz+n te:w) nn94 e. 9wubrdY, 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 uniform disks of eqm2qsne+ )s z (ajp0+av3x bof0 llzx*2ual mass each are mounted to rotate about an axis fixed through the c2 l+*x03psaqnejavs0zfxmb)2 ( zl+oenter 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 disk4/0 krie 6uvmds, X and Y, have equal masses M but different radii such 0 ed6 rkui/4vmthat $r_x< r_y$. 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 cylfcccz 7gs-l29 inder with a mass M and radius R is pulled by a horizontal force 9f clczs-c g72F 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 rt+uzv*85uzkb adius R rotates clockwise about its center with an angularv5uu btk*8zz + 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 mmlzzv s::gc2l)ku0j7; oyhm8 ass M=2.00 kg and radius R=10.0 cm is connected 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, strez:7 lz20j:8lcymv m kguhs; o)tching 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 sinbgtrxj 0043jr3 xrbg4gle engine plane are turning 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 as4 b gjxjt br030gxr4r3 the pilot tries to make a sharp lefthand turn.