12.43: Several forces act on a rigid body. If the resultant (net0n.pf :cq p nfbyn5tmq3v. g26) force on the body is zervn2 g:.nn qtc63ybq 0f.fm5pp o, which one of the following statements must be true?

  97.39: A cylinder free to turnaround a fixed axis h:mz ,ugo4xo;m76 zrir/cygf . as a string wrapped around it as shown to the right. The string is pulled with a force F equal to the cylinders weight. What is the acceleration ofrg7 zgyfo6oxz;m:im/,uc.4 r the string?

  16.16: A uniform stick is fixed to rotate about an axis through its cu bf5y 4:80 vcjaw:xwk(cy/+ljx k xc)enter. The stick starts wk ywu):cxk (:v/cjf5c0xjaxlb+y 48 from 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 kinetic enp5p1 * 6i7keymp4 vyglergy K when rotating with constant angular velocity. When the lg k*pyy1i7p 6m4ve5 pangular velocity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls wio*/ *f b jjyla1nww5b/thout 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,:w6als sq6 i5f 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 disk8t6t7ki-inoy xgt31 z and an ideal uniform ring each have mass M and radius -1on8i7yg 6z t kt3itxR. 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 $μ_disk> μ_ring$.
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 each zaq4c:nof0e y( m.du3 have mass M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. The coefficients ofdu (c0qoa .4nfez3 m:y 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 rollhyxjse 6 rn vo 6,i(:6xc.*bygs 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 as i gh*esnxxr yjc iv.: 6,b6oy(6t rolls up the incline?

  14.43: A long rod of length L is pivoted about its left enmuf if5c/3 rlf 2he2/vd. It is released from an angle θabove the horizontal. What is the magnitude of the angular acceleration of tlmr f32e5vcu2/if h/fhe rod about the pivot when the rod is released?

  15.46: A uniform rod of mass M and length L is fixed to rotate about a frictiya:*khd4 1k asjh2xq k/jda37onless 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 pivota qd* 3dkjksyaj:a/xh47h2 k 1. 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 length L is fixed to rotate about a frict/ ughv s;m*h.6dhclu p d)gg/1ionless pivot located L/3 from one end. The stick is released from rest incrementally away from being perfectly vertical, resulting in the stick rotating clockwise aboug; v.6umdlh hsgd/g*uh/ 1) pct 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 unh;hc6s d.8pgbjvn, s.iform cylinders with equal radii on the end of jn 6 ,p.dv;.cssghb8hhis 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 ,ja:i 6j3hb ohr:t2r eo2vhy.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 diskvxi z+nt8(s1r6pcye+rlgp1z xu4 m gy:6: ib7s of equal mass each are mounted to rotate about an axis fixed through the center of the disk. Each disk is initially at rest. The r+sn i( zy+utbl8r6pgcp: m ixzv41x7 :1yre6gadii 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, .z od/0.u ldkhhave equal masses M but different radii such hk du0./do l.zthat $r_x< r_y$. 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 by a hj re 4tjg- gl9*1h9ox0rpkaa 0orizon rhgatjlrg1-9ej* 4kx o0p 0a9tal force 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 lrl lzn*/ bzapvtu-ep65i ,13 and radius R rotates clockwise about its center with an anga 15-nlebp6 t/urzpvi3l,*lzular 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=10.0 cm i a,bd3mve+8m ns 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 rolls without slipping. What is the speed of the center of the cylindedbn3a+ emv,8mr when it returns to equilibrium?

  01.39: Suppose the enginn*ap9*30u) gaxl;a9;l sk8 em jhwcixe and propeller of a single engine plane are turning in a clock wise direction with respect to the pigawxpa 0)9*3ak 8x 9lhun;j* ;lismeclot. 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.