12.43: Several forces acq1 xjk7)rte4:qmdw 4 wt on a rigid body. If the resultant (net) force on the body is zero, which one of the following statemendqww e7jm tkq r4x4:)1ts must be true?

  97.39: A cylinder free to turnaround a fixed axis has a0s*r fq3scya yun;/c) string wrapped around it as shown to the right. The string is pulled with a force F equal to the cylinders weight. What is thcu ) ;f3asynsr */yq0ce acceleration of the string?

  16.16: A uniform stick is fixed to rotate about an axis+mj8 d.snn t4rpeky 7w4uvum evs*;4o1t3 s4s through its center. The stick starts from re74se4to n+.83 sws v4eskd4utn m1yvu;mrp*j st 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 rotating with con.hijt1 g cx;:: beg8vp4hawq-stant angular velocity. When the angular velocity is rej:x -ewgbvt;ig1 8.a :hhp4qc duced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere r3l t78zal2fae ksge3f9so)u9olls without slipping 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 has mass m, radius r, and rotatiq 4 c9p:rto5nywfo5d) .bymlx2+ +wsbonal 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 disygzee1y 7:2yylj l7 q0k and an ideal uniform 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 and ring witelz gqy21 y7 :jy7yel0h 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 mass ;qmmkdm 8kz66eszs r- 8l)ho*M and radius R. Each object begins purely rolling without slipping down a rough inclined pla) mmezs 6r6kshzd88ql; mk* -one. 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*6b hgyb :dt.d. Which one of the following choices best represents the type and direction of friction (if any) acting on the cylinder as it rolls up the incl6 ybb.:tgd*hdine?

  14.43: A long rod of length Lwhzlxd *kf s9iaa0p9g5 i ;:5p6 +dbbn is pivoted about its left end. It is released from an ax*bpz9gslibf niaw05 ;h5 6dk+ a9d:p ngle θabove the horizontal. 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 is9sdf8yp--jbw hig +l hcw03 *s)qfsl7 fixed to rotate 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 pivot. When the rod is horizontal, what is the magnit lsbwy-cw 3di *s ) h+jph7ffl9g-8sq0ude of the tangential acceleration of its center of mass?

  16.50: A uniform stick of mass M and length L is fixed to rotate about a fri72if5qcobv* 3 d:d9 lzk+kway8b( sll ctionless pivot locatykdc 7b*k9f:a+ ld2vwiz3l5 lqo sb(8ed 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 of three long uniform cylind5 yob-fwse/ uyx;6;s0bo,pmr 5f1bqyers ;b;1x6-soqb/ wbr,pffe 5ouy msy0y5 with 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 a i(rkv(ns*qjgl4p j65ndY, 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 tagf;uk6 y.p1 grm 1c)an axis fixed through the center of the disk. Each diskrf;ptyuc6g11m. gka) 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, have equal masses M but different rb;/kq :;o y/ pdnrylk4jd j9l3adii such tha;ky 9ddjb l:rn4y3 /; /pojkqlt $r_x< r_y$. 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 rad q x;ehpq1 6loxza+y53ius R is pulled by a horizontal forcezq xxh6p;qa1e35yol+ 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 :srdj ,fwx6n6of mass M and radius R rotates clockwise about its cente ,rnwxsj6: 6fdr 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 massz 0/149jw fky ts;b3x-pwxgm h 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, 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 returns4x19yh;k0 tw -pwb 3zx/ jfgms to equilibrium?

  01.39: Suppose the engine and propeller of a single engine plae( sudbkfy*la3: m53i ne are turning in a clock wise direction with respect tmse*(: 3 lk5ui3f baydo 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 sharp lefthand turn.