12.43: Several forces act on a rigid body. If the resultant (net) *f f0bf;fh q/kforce on the body is zero, whiq;f*fffk0/ hbch one of the following statements must be true?

  97.39: A cylinder free to turnaround a fixed axis hig m gxx7+m6jn,lz(tm8cnz(q k+u7l 0 as a string wrapped around it as shown to the right. The string is pulled with a force F eqll+ mucm7x+ k 6ztimgxj 7qz(g,0( nn8ual to the cylinders weight. What is the acceleration of the string?

  16.16: A uniform stick is fixed to yzpl1bya45 2 jrotate about an axis through its center. The stick starts from rest and rotates through 2a4zypb 5 l1yjan 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 blabt n:yd n (1 61,zactvmw4wk-ayde 74fde has kinetic energy K when rotating with constant angular velocity. When the angular 71nvz nwyfmc k4:dw-ty6aaed,t4(1b velocity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slipping on a f+ovu7 u gp9/h8lkxu8ploor 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 ha:b/0hp nkd,h3a;sqvw0he : b xs mass m, radius r, and rotational 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 unsbsn 5ps,gn;d4e9p)hp 0-xf g iform ring each have mass M and radius R. Each object begins purely rolling without slinsp 09bp;)-,fs4es xghdg5pnpping 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 andub q779npdlq ; an ideal uniform ring each have mass M and radius R. Each object begins purely rolling without slipping down a rough inclined p bd9puq7nlq;7 lane. 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 o.j 7qbj, +ta6 3s lvaro5-:hmk nmnke(n a rough inclined plane. Which one of the following choices best represents the tbqm jhn.7tksovjn 5,:r6k a +a-(lm3eype 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 end. It is release1:v4a4yvl lya d from an angle θabove the horizontal. What is the magnitude of the angular acceleration of the rod about the pivot when the rod is l:va 4vyay1l4 released?

  15.46: A uniform rod of mass M and lengt+.u1smv xhw 4/cr*ukdh L is fixed to 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 rod rotating clockwise about the pivot. When the rod is horizontal, what is the magnitude of the tangential acceleration of its center of mas4wd/+kmu*1x vc.hr s us?

  16.50: A uniform stick of mass M and length L is fixed to rotate about a frictek.8q) g 2cc, e ocsx4sczk:8nionless 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 theee) .g 84: s28nz,xk socckcqc 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 cylinderss zt; :)*ekagz with equal ra :;z*gze)t askdii 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, havhs(9tm 7fa c db )4xm)cd0id,ve 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 mou3 aq7b-k q4dywnted to rotate about an axis fixed through the center of the disk. Eadqk-qw 3y7 4bach 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 equalt)okvl4 tz; :u masses M but different radii such tho zl tuk)4t;v:at $r_x< r_y$. 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 ahcn2ikn+hbr: um ,l2/ mass M and radius R is pulled by a horizontal f/u+m n2 hhk, nb2rilc:orce F 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 mase)p p )vl1 xhfsi): 3pbhq)v6rs M and radius R rotates clockwise about its center wit bihp)eh3f v: )lps)p1q6rvx)h 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 cylin 3zvsrjp1so +. nvje )*7rkbz(vk6;u ader 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 from1s7+p*( 6kvnzorev;b3 zkaj) rjvus. 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 turning inejvby/ql8/ju(+y;ew:an2 yk a clock wise direction with respect to the pilot. The gyroscopic action of the monj2/jyaw;y e(ylkeu+ b /qv8: ving parts will cause the plane to move in which direction as the pilot tries to make a sharp lefthand turn.