12.43: Several forces act on a rigid body. If the res:( yk2ccl ke2bultant (net) force on the body is zero, which one byc2 ek: l(c2kof the following statements must be true?

  97.39: A cylinder free to turnaround a fixed axis has a string wrapp1 jqng+ipy/ i-h rat2-ed around it as shown to the right. The string is pulled with a force F-qgti2 pi -y /+jhran1 equal to the cylinders weight. What is the acceleration of the string?

  16.16: A uniform stick is fixed to rotate about an axis thro*br,ri,br/wlsz kk k( r2. qw)ugh its center. The stick starts from r. wk,q)rbz2 ,lbks/rrwki *(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 1hp3 luzz.dncf) 5nd3kinetic energy K when rotating with constant angular velocity. When the angular velocity is reduced to onedzn)ln3zf.5c h1du3 p-third, the kinetic energy becomes

  12.33: A solid, uniform sphere riec * lp47 92b i-odjzkdr*/kaolls 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 aj )t5c. gjuk;o-to6v, 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 6iizd,4 )9 fl tl0)qbf)rdhcfand 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 ,fi )lqr 0tdb c64df 9)h)iflzring 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 amty b :u22l+7xzac dk.zb) /iond 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 incline are /.xcbmyidzba2+k )lzu7 :2ot $μ_disk> μ_ring$.
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 rolkeh(7:4 zip o4euhn, :.vukhm03lcx w ls without slipping on a rough inclined plane. Which one of the following choices best represents the type and direction of friction (if any) acting on the cylinder lxcz: uw k4hv7ho:.mn0 (p,ih43k eueas it rolls up the incline?

  14.43: A long rod of le3w kl4 vu0qkzr;wudoerd. r21i;0bw,ngth L is pivoted about its left end. It is released from an angle θabove the horizontal. What is the magnitude of the angukr2vkrw;udowwie 1lbu0r d0q4z3 ,.;lar acceleration of the rod about the pivot when the rod is released?

  15.46: A uniform rod of mass M and length L is fix0)q-llq2 w qiws 9mkb/ed to rotate about a frictionless pivot located L/3 from one end. The rod is released from rest incrementally away from being perfectly vertil9w0q i qq)mk2bslw-/cal, 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 nf5bm,tk 3x(z 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 clom3b x,(k5ftzn ckwise 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 uniford+ mr ,l 7r xoavrh9bwe0*el-,m cylinders with equal radii on the end x l-rw 9v*da,ee07rlhomrb , +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 dis45 us x:qakn63fpe w7tks,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 mok v2v)y s;qs9*yn4sxounted to rotate about an axis fixed through the center of the disk. Each disk is initially at rest. The radii of the disks are);vs9s4v x*s y2q nyko $r_1 < r_2$. 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, h4yu7c ymh yn+*ave equal masses M but different radii such thy7nycm *hy4u+at $r_x< r_y$. 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 pulled byq oob5xq:myba-3zs8 b -xq +)c a horizontal force F acti bmzb53co- yo)+qq s:b-xq x8ang
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 radius R ryemb(jx4ggqqv/vl+.) hs8 qa 7 n)8 whotates clockwise about its cente4hmwg8y 7l g qsvej.a 8))(nb+x/qvqhr 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 solii51 0uo*4b:le nv8woy njyom*d cylinder 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, stretching the spring 1.00 m from 0nj *i 8oo5mw4nuvob1yley: *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 t 05pd4c b02(+bnwx4w9ybkanc ziwl,wurning in a clock wise direction with respect to the pilot. The gyrolb2aw0 iww d ,c5py0n+xbnbczw(94 4kscopic action of the moving parts will cause the plane to move in which direction as the pilot tries to make a sharp lefthand turn.