12.43: Several forces act on a rigid b0m v aaa w2iq1ll,j4c;ody. If the resultant (net) force on the body is zero, which one of the following statements must b14maaw vlli2ja ,qc ;0e true?

  97.39: A cylinder free to turnaround a fixed axis has a string wrapped around iebtgmk pa:nc+j9 8u(,t 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? ub+ct9a pg :mjken8,(

  16.16: A uniform stick is fixed to rotate about an axis through its center.eh x4jhme-uf+4.k2rkl4f5qd f 6lzsc,3 )gdb The stick start)hlbs 4e 45 -d.4kfrfe h cum,f 2zkxjq+lg36ds 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 rotlwn9d5 ux:xkv0 hl7du,(b 6ypb9n zs 0ating with constant angular velocity. When the anguxp9wy bx70 ( 0bv 6nduzlu5l,hnk:ds9lar velocity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slipping on a floor along thux3f4./g wag -85a,js rykembe $+x-axis$ (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 maoe8c5du099 ;v pqmljo ss 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 solid disk and an ideal uniform ring,ct2h ka*rz+ g 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 dak* ,r2g+tzhcisk 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 pg51; ge gi.oxdisk and an ideal uniform ring each have mass M and radius R. Each object begins purely rolling without slipping down a rough inclined plan1e5ogix.p; gg e. 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 slfc bb/9f4*5yfgvs+ gn ipping on a rough inclined plane. Which one of the following choices best represents the type and direction of frictio/5n vb b4*fgfg+c9sfyn (if any) acting on the cylinder as it rolls up the incline?

  14.43: A long rod of length L is pivoted about its lef7oub2.w1 vja;/s9 jm vj ci2kft end. It is released from an angle θabove the horizontal. What is the magnitude of the angular fv js.7c2j/jk9a1bu w2;imov acceleration of the rod about the pivot when the rod is released?

  15.46: A uniform rod of mass M g4fu641xamrit.k iqen/py 1;and length L is fixed to rotate about a frictionless pivot located L/3 from one enirx;m 4i n e6atq1k1ug/4 fyp.d. 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 tangential acceleration of its center of mass?

  16.50: A uniform stick of mass ,trlu6nlm8l5 ajchlb k/, :8 mM and length L is fixed to rotate about a frictionless 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. Whjt /8l 8uc ln :,6,rmlbmhkl5aen 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 three long uniform cylindeo*5jqqe5 kyy nr .40fnrs with equal r n j0qyqe.5f*5r4n oykadii 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 di;/hssax0jz5s9,23e 6r b i6n zakjw basks,X andY, 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 equal mass each are mounted to rotate about an onz ob3wqnrh(:;0)yb axis fixed through the center of the disk. Each disk is initial)0 wnorn;zh 3:b(obq yly 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 awtzkv;.b2scp w0 z6h 1)xaqi 6nd Y, have equal masses M but different radii such )0 c6;wzvb1 .6sx wzqt2pih kathat $r_x< r_y$. 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)id+dpn1gz-q tyl 2d6 mass M and radius R is pulled by a horizzdyqdl t-pd2) 1nig6+ ontal 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 mo zpvbnp6j3(*ass M and radius R rotates clockwise about its center with an angular speed bzp n3 jp(ov*6 $ω_0$ . 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 iv)y6 baw tglj1m2 ;(xjb-o1eos 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, stretching the spring 1.00 m from equilibrium. When released, the cylinder rolls withoo2ej ot 1ja-;6 yb(wbg) ml1vxut slipping. What is the speed of the center of the cylinder when it returns to equilibrium?

  01.39: Suppose the engine and propeller oaqoq5li-zp sj+0 (u k:f a single engine plane are turning in a clock wise direction with respect to the pilot. The gyroscopic action of the moving parts will cause ths0uo ik(aq:qp5+-zjle plane to move in which direction as the pilot tries to make a sharp lefthand turn.