12.43: Several forceyc7 h:m4yate4k hq5 l/s act on a rigid body. If the resultant (net) force on the body is zero, /lyemh4qth: ak754 yc which one of the following statements must be true?

  97.39: A cylinder free to turnaround a fixed axis has a s 8v24-wie rz959k:zotpnmp2 hcmnmd. tring wrapped around it as shown to the right. The string is p9rk:.9 v-w54do n pinpmhm em22zt z8culled with a force F equal to the cylinders weight. What is the acceleration of the string?

  16.16: A uniform sticx 3u6v 57sxtllgg p8c 5c*gk8/a 0coxik is fixed to rotate about an axis through its center. The stick starts ui 0xc5a s85g t3/ggpo7vll68xxc*kcfrom 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 energy K ki-8glix amd0-ubo7; when rotating with constant angular velocity. When the angular ved il7u;bgo i0x8--k amlocity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slipping on a floor along the ec+g5/lgql 1 z$+x-axis$ (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 rotational ineroth 3 q;hj:q-itia $0.5mr^{2}$ . 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 each haveksnm +sjql: c)tg8 m/7 mass M and radius R. Each object begins pug j7s clt:sk+/qm8mn) rely 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 b .stf)82gs5pkl ji/4jk( dvmuniform ring each have mass M and radius R. Each object begins purely rolling witgvfb i.p4/j2 m) (jlsk5 kdts8hout 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 plane.5nq2frw s41 dv Which one of the following choices best represents the type and direction of friction (if any) acting on the c5 sdv1wrqn 4f2ylinder as it rolls up the incline?

  14.43: A long rod of length L is pivoted about its left end. It is releaso+3- cmyho0a3e:mnv u ed from an angle θabove the horizontal. What is the magnitude of the angular acceleration of the rod about the pivot when the rod is released? -vn +a ume0yoc3om:3 h

  15.46: A uniform rod of mass M and length L is fixed to rotate about a f/iavn,(z 4 po ,;i91kluiohzu rictionless 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 tangentiaii l 1nuiz,z(u9ok ;ph/v,o a4l acceleration of its center of mass?

  16.50: A uniform stick of mass M and length L is fixed w+zj9rde iq5 d q-5ds+to rotate about a frictionless pivot located L/3 +55zeqw-+drqijd ds9from one end. The stick is released from rest incrementally 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 verticah4 f-+flox (,t p :lbyyyj78hllly each of three long uniform cylinders with equal radii t lb+f8yyl:yh h f(px4j,o-7l 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 disks1ppm3 g23m2d5ubc lmk ,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 masmw hc/r)isuc2frli305 fse39 s each are mounted to rotate about an axis fixed through the center of the disk. Each disk is ini3c)3hc5rl si fu9emsiw/rf02 tially 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 anigm(*,u m m lz*usds,;d Y, have equal masses M but different radii such tha(ml ;msu,g,**dsim zut $r_x< r_y$. 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 cylin ),-i7vgwqhb srx6t p-der with a mass M and radius R is pulled by a horizontal force F 6ptqix) ,7grwhsv--b 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 and radius R rotates clockwise about it)5xewvtu d;(ps center with an angular speed 5et(u)xwp;v d $ω_0$ . 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 is conn/ uashtpcu+c0) *2 qjnected 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 equilc)c ja0 u2/utns+pq*hibrium?

  01.39: Suppose the engine and propeller of a single engine plane ar.1lf pbq7 n d*dsbc2g7e turning in a clock wise direction with respect to the pilot. The gyroscopic action of the moving parng1d7 plbq *.2csf7b dts will cause the plane to move in which direction as the pilot tries to make a sharp lefthand turn.