12.43: Several forces act on a rigid body. If the re7/al3bc7 tuthdu2 9 mpsultant (net) force on the body is zero, which one of the folcbh 37 ttu27dlpum /9alowing statements must be true?

  97.39: A cylinder free to turnaround a fixed axis as19k xo u4j4nhas 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 of the strojnsk914x 4auing?

  16.16: A uniform stick is fixed to rotate aboulutv: r5darjp06.x.pt an axis through its center. The stick starts from rest and rotates through an a05t6 jruldvr..x app: ngle 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 kineq,f4x-n+ oshej v(ck( tic energy K when rotating with constant angular velocity. When the angular velocity is reduced to one-third, thchovqj( +f4,kx-s n(ee kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slipping s74j i1s hrk+ jl+id-son 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 7 i3 o84xwfvkix 4pwqflf /19erotational 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 soli u ;6f lothd2(37tmpykf*q/kb d 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 u;oq tt/f7b y 2f6l(pkk3h*mdcoefficients 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 eachdw e ue6;6la0a have mass M and radius R. Each object begins purely rolling wit eladwa0u; 6e6hout 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 8s8dot-f13o-pj(*y a+wv6bcd jk gu j rough inclined plane. Which one of the following choices best represents the type and direction of friction (if any) acting on the cylinder ajkwvu3 b6 o8 pds8y-1- ot g+cjj(fda*s it rolls up the incline?

  14.43: A long rod of length L is pivoted about its lev5 7k1ueny +k1eun: mnft end. It is released from an angle θabove the horizontal. What is the magnitude of the angular acceleration of the m1unyn5e 17k:eukv+n rod about the pivot when the rod is released?

  15.46: A uniform rod of mass M and length L is fixed to rotate 7st)11kk .ydz qhye1e about a frictionless pivot located L/3 from one end. The rod is released from rest incrementally away from being perfectly vertical, resulting in7)sq1.yyt1h e kz1ek d the rod 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 fixed to rotate about a fricti8dqotgo3dbi ,9bx(b 4onless pivot located L/3 f 9(d,oqog bd8xbt i4b3rom 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 vertically each of three long uniform cylind(kgz ;itk, thvz.s 8z: 5k2qfmers with equal radii on the end of ( k8;mvt 5.:tzgk z,h2siz fkqhis 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,yq9; i p1d03khzd6qvdnk/w 2g 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 u kg(/yw w/io-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 ryokuww i/g(- /adii 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 massesrmta6 j9 p1)uq M but different radii such thajp rt9q)um1a6 t $r_x< r_y$. 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 cylindyq r/8l( 80d3mn *cec0:deq ymev kg9qer with a mass M and radius R is pulled by a horizontal force F actin(0ymlq0c / v:qde3q8 *nryeeg 9c8 mkdg
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 ao(lob+ ) zefy(bout its center with an angular speed lzfy)( o (b+eo $ω_0$ . 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 maf+dqw548.g-q) csfy qv-xa skss M=2.00 kg and radius R=10.0 cm is connected about an axis through the center of the cylinder to a hocdqq svsf8aw-)g+y4. -5 fxkqrizontal 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 and propeller of a single engine plnnh5tfa h 1;jqk-y/t9ane are turning in a clock wise direction with respect to the pilot. The gyroscopic action - nh5hn;qt9y /kf1jta of the moving parts will cause the plane to move in which direction as the pilot tries to make a sharp lefthand turn.