12.43: Several forceb-m f(, p*eusgll2us99: o yhqs act on a rigid body. If the resultant (net) force on the body is zero, which one of the following statementlpg, u92*ys -efu(lm9hos:qb s must be true?

  97.39: A cylinder free to turnaround ax7(cb 3mss b*t fixed axis has a string wrapped around it as sb(bts 37m scx*hown 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 fixed to rotate about an axis throu(ct c7f*lpb h2 jx5z.zgh its center. The stick starts from cl(jfx 5.czb 2t7*hzp 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 ha qy2 j9g4u8p9u*) e mjfnnj4qes kinetic energy K when rotating with constant angular velocity. When the au9 2j8 j*qqyj4u pmef nn94)gengular velocity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls withoufr )9 iru+zb,rt 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.rk iw92/z.yhikpurn.7 g o b; 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 axsfxsva33qc5c x brz i6 -2oy9j47q)knd 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 with the irzc3)x-3 cf bqxi2k 9ysvo5764sq xja ncline 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 ided nt dbwa-ksoj356;eu 8-*zrsal uniform ring each have mass M and radius R. Each object begins purely ;3rdtb-jaek58 z*w6 nu sosd- 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 cylindebq3uek7oc.dqkfe):9 c1s :xdm yx+n 1 r rolls without slipping on a rough inclined plane. Which one of the following choices best represents the type and directioe)c3+b 1msqe.xk:nfx 9y7 ko1 d qu:cdn of friction (if any) acting on the cylinder as it rolls up the incline?

  14.43: A long rod of length L is pivjtjqvar. 4-/nr 0b9 nmoted about its left end. It is released from an angle θabove the hbr9.j/- 0 jnrt am4nvqorizontal. 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 a y75ousw kl;(+3b mrv:gkyk/b):mtev bout a frictionless pivot located L/3 from one end. The rod i :e/gotl +ru5;kyb s7m:v(wkkvym)b3s 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 M and length L is fixed i*;pvfoiv9hfg* d) i6ivbc86to 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. When the stii ff*v6hi*8;vo cg i69dbvpi)ck is horizontal, what is the tangential speed of the center of mass about the pivot?

  06.24: A person triek.gz rch los.8kz)e:txm;,h: s to balance vertically each of three long uniform cylinders with equal radii on the end of his f,z):.e:k m.g z ;lk rthcxsh8oinger:
• 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 drozquqc2 hq)j02g w((isks,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 ea)xoliv/yu06 7dsd b o+ch are mounted to rotate about an axis fixed through the center of the disk.0+x v/sbu li7)do dyo6 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, have e: q -52*lscwhj (aipwpqual masses M but different radii such that*ihwpcq(l5pjaw:s2- $r_x< r_y$. 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 pullfvt * 3z9pgio)ed by a horizontzp9gi)vt *3 ofal 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(t.0nsr 7urmtyt d34d of mass M and radius R rotates clockwise about its ( m7t4dus n.r tdyt3r0center 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 ra uxbk63ybbo0z;t2zr* 08 u jbqukj)d:ah9n) a dius 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)3z0:6ob dx b8uukuajtnzjq2rabh0 9 );bky * speed of the center of the cylinder when it returns to equilibrium?

  01.39: Suppose the engine and propeller of a 2wz e2 j7l6hvzsingle engine plane are turning in a clock wise direction with respect to the pilot. The gvehwz z2lj67 2yroscopic action of the moving parts will cause the plane to move in which direction as the pilot tries to make a sharp lefthand turn.