12.43: Several forces act on a rigid body. If the rd-*bzqf ag /r)esultant (net) force on the body is zero, whiqrgadz-)*b f/ ch one of the following statements must be true?

  97.39: A cylinder free to turnaround a fixed axis has a ,09j xv*mxstp nnkxwp7+9kn 3string wrapped around it as shown to the right. The string is pulled with a force F equal to thep x,j09p+wxn *n t9 sv3n7kkxm cylinders weight. What is the acceleration of the string?

  16.16: A uniform stick is fi c.a/sm 7kz;xpxed to rotate about an axis through its center. The stick starts from rest and rmp;s7 .a/xckz otates 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 constant an*ud(gcp (qvpcf50tl * gular velocity. When the angular velocityt5pcpd(* v0f(qgu *l c is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slipping on a floor alon gg5tn;1nd m9 zbv+4b*ssdo0dg 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 ma54i,muw jmzuz4 yd1y,ss m, 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 uniform ring eacd b9;t b+r:0pvrkijfuq)h 6s zrb :1b3n9zs3z h have mass M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. The coefficientkq tsj13b9n :0rrdz zb3 u)v+z96 ;rphsbfi:bs 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 soli9, 6/lsulzc6jyxl s,ed 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 coefficienxlysc,, l6l ue jz/s96ts 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 slipping on a rough;4+ vpc:ltbw8d s1bc p inclined plane. Which one of the following choices best represents the typec4t1p8 bs;vbc dw+lp: 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 entt s2 y1et-h 7;vr9megd. It is released from an angle θabove the horizontal. Whatstgemhv-t79 r; ey t12 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 fixe;v.c.q vji f)wd 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 pivot. When the rod is horizontal, what is the magnitude of the tangential acceleration of its..jwfq ci )v;v center of mass?

  16.50: A uniform stickssliunqh ;4 :q7/3gz.skl6l ,x,fhan 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 incrementalz4qg3naihlx.hqkf/ s :7 sl ;s,ln,u6ly away from being perfectly vertical, 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 vertically each ko360w*cx bkx6c2hwqof three long uniform cylinders with equal radw *wkocx6qx0bhkc6 32 ii 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 disksl0 2t- 5pahftnu o219azxg2bu,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 mat( vrx,7 n8lm f2j0kaa.y, nmi2xb 2a a-4wquyss each are mounted to rotate about an axis fixed throughx24 y80auivkan2 m,twrnm(yqxl-7.2j f ,a ab the center of the disk. 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 equal masses M but different radii x :28ckrf3n0 x jxj64ccq)ovsdd9 a1qsuch thcjc0 a rx168njo)d3 qfxdqxvs:c4 k92at $r_x< r_y$. 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 phi07c 3w7fbyby a horizontal force F ac p3bcfiwy7h07ting
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 massl q57xjy sd f60bfy2l+ M and radius R rotates clockwise about its center with an angular speed5bqf+dyj6 ll7 fy0 x2s $ω_0$ . 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=2.0)bbmvhy)v 2b yyt(-p00 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 equilibrium. When released, the cylinder ro2pyb y)vmb)0v b- hyt(lls 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 engi28 35qe qppl4ar ,c2hgc:u orpne 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 in which direction as the pilot trq2p:p 5q34lp82ccorue ah ,gries to make a sharp lefthand turn.