12.43: Several forces act on a rigid body. If the resultkw0uu56 m) mrvant (net) force on the body is zero, wh6mvwumu)kr 50ich one of the following statements must be true?

  97.39: A cylinder free to turnaround a fixed axis has a string wrapped arour,ealpm;q y o/j a8*ex7g.k/m 42e:dnrw: ullnd 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 striny;lmkere paea/ rx4lqju.nw7 8*om : /d: 2,lgg?

  16.16: A uniform stick is fixed to rotate about an axis through 6hp65b cu54jzm+lojeits center. The stick starts from rest and rotates through an az6c+h5ob jmu 4lj5e6 pngle 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 kin * pplr/ 239cnp;(phubcxk2m4nn yul/etic energy K when rotating with constant angular velocity. When the angular velocity isc/9ury3 lp/lpnc4p k2unn x b*(2hmp; reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls wgu0m*8u mzq5:bng :hh ithout 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, and rotat32pnhssze8dj;l 76d g ional 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 unifo25rn3ku k xt w4hpyx )ap,j9+brm ring each have mass M and radius R. Each object begins purely rolling without slipping down a rough inclined pl9),pk 4pr+ 3awt5hynuk 2 bxxjane. 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 ider-u .flesyn+5 al uniform ring each have mass M and radius R. Each object begif5eru ys.l+n- ns 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 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 inclinedt kwf90sh/z )h6jbed6 plane. Which one of the following choices bes9hs6de 0 /hbzf)wjt6kt 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 leftqqthl-jw e6n./j f f7gwiew. 7*;4ojd end. It is released from an angle θabove the horizontal. What is the magne gl d jwh6f 4.7nq/qwj.oj- 7w;*ieftitude 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 fixed to rotate about a frictioqsz/ c)ktp w44rk:620wfe yjn nless 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. Whp 4k4:t)fkc2r s/w wz e0jnyq6en 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 isuyjw*ip ;y7zzk8pm. . fixed to rotate about a frictionless 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 about its pivot. When the stick is horizontal, whwpz.p ;j kzyi*ym u7.8at 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 cylindev*f:vhozijac6 )q d81 rs with equal radii on t*ofiq: 8vza6 )cjvd h1he 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 disks,X t,*li-u+ 9yyy,x c+bbqc0 uy oiay)+candY, 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 mass each are mounted to rosglx, p va-1u2tate about an axis fixed through the center of the disk. Each disk is initially at rest. The radii of the dxu,2v- lag1psisks 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 equaljmdi u/.eo o0vhi9uccs /,5s* masses M but different radii such mcsv ,/* o/eu.ojhdsiic0u5 9that $r_x< r_y$. 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 with9h vgwy9y 6i*s a mass M and radius R is pulled by a horizontal force F actingihyy9 6*v 9wgs
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 itshy) h2ts0r1hz z dq7thu)+8qqpf 05aw center with a8 1 hh72uzh0adfqtw+)r0s 5yq ptzhq)n angular 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=10.06fo /*hhw:jgevwm7+ t cm is connected abo vjhtw: *f/ m6ohw+e7gut 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 equilibrium?

  01.39: Suppose the engine and propeller of a single engine planep0m7a7vgd mfhjh9x 3z1z e**h are turning in a clock wise direction with respect to the pilot. The gyroscopic action of the moving parts wilj1hxm39v7 ghe*mz 0 d7 paf*hzl cause the plane to move in which direction as the pilot tries to make a sharp lefthand turn.