12.43: Several forces act on a rigid body. If the resultant (net) forc d 5i s2w ky0z+yifi0u;1kop-ue on the body is zero, which one of the foli2u +o fziydsku01 5w-pk0 i;ylowing statements must be true?

  97.39: A cylinder free to turnaround a fixe8w j;,kh; 6uvxyg7+ nyiha 1ptd axis has a string wrapped around it as shown to the right. The string is pulled with a force F equal to the cylinders weight. What i;ijkux v;patn+1h gy8yw, 67h s the acceleration of the string?

  16.16: A uniform stick is fixed to rotate about an axis thrpix13 -ymp q1 e-z/vopough its center. The stick starts from rest and rotate-vy-zxppimo/ q p311es 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 when rotating with constant apk.7x**sf8x,va io tangular velocity. When the angular velocity is reduced to one-third, the kinet87sx *aavk.i*fo x,tp ic energy becomes

  12.33: A solid, uniform sphere rolls without slipping on a floor aloour-l2yjrm e-+n sf/ 2ng 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 rotational in;jyc h-g,( zsnertia $0.5mr^{2}$ . 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,cwc18vz rep+ nb:;w s and an ideal uniform ring each have mass M and radius R. Each object begins purely rolling without slipping down a rough inclined pw:p,+ ze1 sn8;bcwvcrlane. 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 ringv d8jezqx4*m 9 each have mass M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. The coe8dex* zqj94v mfficients 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 inpz8/.jvte8 xb6 ulj:mclined plane. Which one of the following choices best represents the type and direction of friction (if any) acting on the /tx:z68jevl b8jpm. u cylinder as it rolls up the incline?

  14.43: A long rod of length L is pivok+qw b ) aga0r*1i6ytuted about its left end. It is released from an angle θabove the horizontal.+g *k )baiytwr6a01q u What is the magnitude 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 fri1y)q qn ijp6zq8j2/ln /jiuc+ ctionless pivot located L/3 from one end. The rod is released from rest increment + iqnz)/ y82jpj/ jluq6cqi1nally 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 tangential acceleration of its center of mass?

  16.50: A uniform stick of mass M and length L is fixed to rotate about a frict5dwmbq 82 yphr zzb)ylues)7y+ -+ .uuionless 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, what is the tangential speed of the center of mass ay ).zsue 5b+rdbpy 7l+yzq)u2wu-h8 mbout the pivot?

  06.24: A person tries to balance verti 592a2b+vl7 8jdh dzi;yjqsd odw3vv3 cally each of three long uniform cylinders with equal rad2yzdb3 + vvsh8 w7;a3j9d j5i vdld2oqii 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 disks,X andY, have masiqbh yx74pgw41/i f1cses $m_x$<$m_y$, 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 rotate -g4ih:4:wta q p oi fah .;b3 r,34alelx6groaabout an axis fixed through the center of the disegt 4ohargb4,4f ali6-h.pq wi; ::ar 3l3xaok. Each disk is initially 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 and Y, have equal masses M but dlwki 8,1plub3u/um 4 lx(rc8(ru.ch tifferent radii such thau kbr8u((.ph1/illrc8 4,cum txu wl3t $r_x< r_y$. 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 pull9 i6 hze17(6wmox(mjf;yxdqlp )v*txed by a horizontal force F actw t(fz)*7plojx;9vx q(hdyme 66xm1i ing
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 Rs33 q6+yoq ugrgp)-en rotates clockwise about its center witpyuen)6- q 3rq+3sgogh an 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 madc7q kwo91tz 4txx 46oss M=2.00 kg and radius R=10.0 cm is connected about an axis through the center of the cylinder to a horizontal spring6zox1 qw ok74t4tx9dc 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 plane are turn1mow9*n;mq jjhz4 r2 jd+u :aning in a clock wise direction with respect to the pilot. 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 td mrnmjjuo124z qh 9;aw:*+jnurn.