12.43: Several forces act on a r0)mn8wqp r: rzigid body. If the resultant (net) force on the body is zero, which one of the following statementrwm8n pr: )z0qs must be true?

  97.39: A cylinder free to turnaround a fixed axis has a string d-xca jtib;v y6)1pxtkolx8m:u ,1;-ea7th y wrapped around it as shown to the right. The string is pulled with a force Fjm1l)e:akd v;uc - yx- 8,p7x;h6t y1otibax t equal to the cylinders weight. What is the acceleration of the string?

  16.16: A uniform stick is fixed to rotate about an axis through its cenh 6wu (:ig6a t64iqibm-v pcg+ter. The stick starts from rest aub+4mgq i6p(igac i :-vt66wh nd 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 co dt;k ;hpslaq k 039t,q8ow2vcs 6d+eonstant angular velocity,kpw6a;;o3 ol 0 t2dqkcve ts h8q9ds+. When the angular velocity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, unifonp6t0 a8fvso h.n tz-.rm sphere rolls 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 rotational inertia gz( y1cz /5r/nyj7 vhm-eg0vx $0.5mr^{2}$ . 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 solim/ y(pk-i vby*d disk 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 coefficiep/ibk- (myyv*nts 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 ea3a(c :lkrlnq; ch have mass M and radius R. Each object begins purely rolling without slipping down a rough inclined pla l:cnak l3(qr;ne. 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 slippiphq.u;( *g( y*)d kam iabv67(d-jyjsicu wi7ng on a rough inclined plane. Which one of the following choices best represents thk(y 7i )dh(vadu s iuqj*b (gcym-6. i;7j*pawe type and direction of friction (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. Idu5) 0r6jeukc hzjne)- /sneu. vs :k;t is released from an angle θabove the horizontal. What is the magnitude of the angular acceleration of the rod about the pivot when the :; je6 5nvs)c0d.keeh)n uukurs-/ zjrod is released?

  15.46: A uniform rod of mass M and length L is fixed to rotate aboubmik qfb +3vxo/x4 (g*t 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 hogk4b3v/b*(xmfq i o +xrizontal, what is the magnitude of the tangential acceleration of its center of mass?

  16.50: A uniform stick of mass M and.q:ws; ysh-/ tsjq2v u 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 clockwisjq2:t yvs su/h s-;qw.e 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 , ls* z)rctc+vnq az50cylinders with equal radivnzz0c+t, cq5asr * )li 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 andY, have massesxx0d z byt8l4 knofdy-3q ci,1 4:,qwo $m_x$<$m_y$, 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 t2jgz3cfz5 k-rq ky bo5n+annxsji7o,c9/)z + o rotate about an axis fixed through the center of the disk. Each disk isxz nb9c gf)3 k+qnjooz+c57,rnyi-2 zask 5/ j 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 equaly,*y 8rh f:nib6s;/8*hpqypp etbx6 s masses M but different radii such that6tp 8 iry6fq;*ph*b,hnx :/sy se8ybp $r_x< r_y$. 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, solidav4 dy yrh86po* * etv4gywr371mfhm- cylinder with a mass M and radius R is pulled by a horizontal force4 rft r6ehhy*dyvo871 43w*vpg m- yam 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 radk vzycdt 7mk7-c3cte 1 .kl4j+ius R rotates clockwise about its center wkk.k7dc l3cmtzcj t7 1e- +4vyith 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 cylind/lijhki 5l6, ier of mass 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, stretchin,6ji/lhlk ii5 g 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 single engine plane are turning in oq0pjaoev;* 7 lj(; nsa clock wise direction with respect to 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 leftq(;onjvs *eaj l0 7op;hand turn.