12.43: Several forces acq21ys9n r/87.d3hxcf3y/vcndfq wdpt on a rigid body. If the resultant (net) force on the bodyn98.d rvq 7yn ffdws q/c3cx/yp213h d is zero, which one of the following statements must be true?

  97.39: A cylinder free to turnaround a fixed axis hari w;, 8/lnph 4zx h.9pbrmws/s a string wrapped around it as shown to the right. The string is pulled ps .,r/;/ pmwn9hwx8riz4h blwith a force F equal to the cylinders weight. What is the acceleration of the string?

  16.16: A uniform stiid4q lx 5hej3,xi67jci/ rw:k ck is fixed to rotate about an axis through its center. The stick starts from resxd : rx4q,jiil kie73w/h5 6jct 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 w4-lezss lgi7(t o m;m5 9sjvolxu )kvf w596:eith constant angular velocity. When the angular velocity is reduced to one-third, the kinetic energy beco96v)4xlmwsek( motugf:5i;5ljozs -sve9 7l mes

  12.33: A solid, uniform sphere rolls without slip4yi47;l w 2/pzmphpx xping 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 mz tbz6z 1mx33a, 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 and an ideal .5 dxqjfgog3w3 ;ab2 tuniform 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 inclinej53g; ofwb qx23.atgd 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 rinv + gkpcwhhba -zk*01ma 4t6n:g each have mass M and radius R. Each object begins purely rolling without slipping down a rough -k6av1ht bk*0 hpg4wz c+:naminclined 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 cylinder rolls wi 7t7 kvhme mhs)9x9vm(d/ft* dthout slipping on a rough inclined plane. Which one of the following choices best represents the type a 7xh)f 7tkmteh/vddsm*m9 (9vnd 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 0bh4hu l ((mvv7g bu qg9.r2rb y;hkf;left end. It is released from an angle θabove the horizontal. What is the magnitude of the angular acceleration of the rod about the pivot when tv;y.b 4b fvkl(uq7ghr;09mbh gh (r2uhe rod is released?

  15.46: A uniform rod of mass M and lengtko-5unqq4v c6 h L is 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 pivnqo4-qu5k6v c ot. When the rod is horizontal, what is the magnitude of the tangential acceleration of its center of mass?

  16.50: A uniform stick of q4 15ego q idwey/1(1dib.cnpmass 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 vertical, resulting in the stick rotating1q wo1dyq ni5b(e/.4de1pcgi 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 uniform7 e.s,g/ 1vrepae w1jp cylinders with equal radii on the end of his finger.e11pas 7g,r pwj/eev:
• 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, have6qrixnq pe /t 9;m7kf- 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 aboutmi;pq o9wo/ dw.t;b v/ an axis fixed through the center of the disk. Each disk is initially at rest. The radii of the diskqpb; //d;om9ovi .ww ts 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 differen)g/up5a- magtwk74zo t radii such o/t7) u a4wzg ap-kgm5that $r_x< r_y$. 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 cy: h vn-zfvra5-wfn kk0/b /ch)yb 6ta)wpl6k +linder with a mass M and radius R is pulled by a horizontal f/k-+)0 nbh k6bt a/vczwr fpfyw 6-kl):h5vanorce 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 masmdol8s3bw8h+ crb3m syg-63s48xt t*9pnky ts M and radius R rotates clockwise about its center with an an*d9mc-nw8kyms 8 3o6s 3hbbp3lsxttgtr4y +8 gular 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 khlvhdp-p*j. cmate 7a(z 6oqt24d5)b g and radius R=10.0 cm is connect6h 4 l(zj cqop.m d-5a)eh7atv*p 2dbted 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 returns to equilibrium?

  01.39: Suppose the engine qw .(*tk0ykp/f i+zfzand propeller of a single engine plane are turning in a clock wise direction with respect to the pilot. The gyroscopic action of the moving parts will cause the plane to move p f z0k/ty+kq.zwif *(in which direction as the pilot tries to make a sharp lefthand turn.