12.43: Several forces act on a rigid body. If the resultant (netbl bzw- 4o)bk v*j6x-n) force on the bodybbjl4xnkv 6*)- bowz- is zero, which one of the following statements must be true?

  97.39: A cylinder free to turnaround a fixed axis has a string wrapped,j t8ejd5d h7i around it as shown to the right. The string is pulled with a force ,5t8 7id djjehF equal to the cylinders weight. What is the acceleration of the string?

  16.16: A uniform stick is fixed to rof 5 *c+ 3zpyfqveas;y6tate about an axis through its center. The stick starts from rest and rotates throug36; fvpzea5+* qyfysc h 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 constan r)h )pvfls 6lp/mr(e,t angularv,s pf pr/)r(el6hml) velocity. When the angular velocity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slipping on a floor alonguo13)e.)v .ukcq0 zxefp : zom 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 rotag6spp :w; xm8ftional 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 8 z0 kpko/a7r;dje0qn*j c*h5wj fqs.uniform ring each have mass M and radius R. Each object begins purely rolling without slipjde8oh0fk z 0rcakqs w; 5.*n7/pqjj*ping down a rough inclined plane. The coefficients 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 a :t,xi48znoq tnd 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:ti 48zxtq o,n 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 78q w.lkh5 cyfaes3 l+rough inclined plane. Which one of the following choices best represents the type and direction of friction (if +fh5k3c a7 8l.swle qyany) acting on the cylinder as it rolls up the incline?

  14.43: A long rod of length L is pivoted about its left end. It is rel;o)eyoe /*khj eased from an ange yoj oh;)k*e/le 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 lengt1qg .,/z c(ze2ho.yrgy4y: j4 j yaemnh L is fixed to rotate about a frictionless pivot located L/3 from one end. The rod is released from rest incrementally away fro1nycze,r za2gym/4h.q.g o(eyj y4j:m 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 .poq8fk,j 3tr of mass M 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 verf.38,jk rpqot tical, 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 verta,r;08.)vp nd sdu (tz e9)obx*f lcxwically each of three long uniform cylinders with equal radii on the end of his vt*x9od8nfx0;) (dlwrpuz base ,c.) 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 *9lv3eog1 tdjndY, 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 o bp 7f/e*w ni9,znkg4bf equal mass each are mounted to rotate about an axis fixed through the center of the disk. Each disk is initially at rest.e 4f 9bwiz,*n7 bkn/gp 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 eqj qe q5,xmdb;k :1qd:wual masses M but different radii such w d,5:mjbk ;xeq qd1q:that $r_x< r_y$. 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 cyl. h4* ;xvhgmdkinder with a mass M and radius R is pulled by a horizontal force F acting gv; kx4hdm*h.
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 rotates clockwi ac/6vn p9g is:qn,kcq zx-2e:):uxswse about its center with an angul) wuz:k2qxxs6cq -neigns v: a: ,cp9/ar 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 radius R=zw+y c1(ayo rbl.0xm i-ik6m010.0 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 bac0.ocylm+ba0iz ix r(w 1m6k-y k, 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 returns to equilibrium?

  01.39: Suppose the engine and propeller of a sing)tlyum:n r+w (rto+b.le engine plane are turning in a clock wise direction with respect to then+m(wu:lr oyt+t.) rb 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.