12.43: Several forces act on a rigid body. If tgtb prp- 4vlk(*)/ srkhe resultant (net) force on the body is zero, which one of the following stat rr4/lt(p kbgk s*vp-)ements must be true?

  97.39: A cylinder free to turnaround a fixed axis has a string wrapped ar2o(vj uz.kj6 ufq quorv+2r 38ound it as shown to the right. The string is pulled with a force F equal to the cylinders weight. What is the acceleruqj.oo2+rfku vju3r (zv26q 8 ation of the string?

  16.16: A uniform stick ij0b(u 7ilxua gg/39mt s fixed to rotate about an axis through its center. The stick starts from rest and rj u/x3iug7(b0t ga 9lmotates 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:6k*3bofphnp9 p /f rg when rotating with constant angular velocity.6 g*n:f opr39 kh/fppb When the angular velocity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slipping o6i7jvv6h: hfrvh1 oi* ;lt b6ln 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, and rotat 1ak gfs oqk(l(vs4 dhc90c)l1ional 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 un,l(7/2lu ybxo nsqdj5iform ring each have mass M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. Thb2( /y7 qldoxs,l 5june 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 have mass M ap vfxgqt +:)8/ 1cwzttnd radius R. Each object begins pft+tct8v): /zpxw1g q urely 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 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 inclined plpbp 6miqwz/l21 5)u weane. Which one of the following ci2b/5w 1)l6pmzqu wephoices best represents the type 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 rjd.p83ok2 dd end. It is released from an angle θabove the horizontal. What is the magnitude of the angdorjd8k d2p3. ular acceleration of the rod about the pivot when the rod is released?

  15.46: A uniform rod of mass M and length L is fixed to b65 w-vdb5v ns:995znbutomg 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 sv5z-5b wg9:vn bn5tdou 96bmrod 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 length L is fixeddz+kgef )4*8u(ok,m f6rpf lx to rotate about a frictionless pivot located L/3 from one end. The stick is released from rest incrementally away from being perfeck6f,p4ume dz l k(*r x8o+ff)gtly 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 vertxj5):r;esu*u pi2 ihrically each of three long uniform cylinders with equal radii on the end of hi *siu;i j)2 ueprh:5xrs 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 andY, have massest+0lixc4cj e8e4 y-d z $m_x$<$m_y$, 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 diskss(m 0bcdfb9z8 hqw w,smmu8* k,jh-o) 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 )o ms*ju,9hq,d w-(0 z8hcmsbw kmfb8radii 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 bvgec+: m,os+( h in(rmasses M but different radii such thv+,n: (hbm e+sicog(rat $r_x< r_y$. 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 homprro;,ptx8 )rizontal force F actinp;tx)rm ,p8org
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 clockwise about it;drkzip qd p 6) 5tj+d9wnt:j6s center with an angular sdq ;d)+5iptk djw9rn p6jz: t6peed $ω_0$ . 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 c96n)rwlt1odsuuhz 4f)sh e 25ylinder 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 equilibrium. When released, the cylinder rolls without slipping. What is the speed of the center of the cylinder when it retur ers5924hfut6 nwslh)u)zd 1o ns to equilibrium?

  01.39: Suppose the engine and propeller of a single engine plane are tur0.t)wxjmy., b4 +jj7lo tktn /x-jpwwning in a clock wise direction with respect to the pilot. The gyroscopic t)xx ntw,7 m yj.. j/4tw0bp kjjw+-loaction of the moving parts will cause the plane to move in which direction as the pilot tries to make a sharp lefthand turn.