12.43: Several forces act on a rigid body. I/,u li)2sse0 k.qnpf hf the resultant (net) force on the body is zero, which oneienk)s l2u sqfp 0/h,. of the following statements must be true?

  97.39: A cylinder free to turnaround a wsm:2pt4f xag9 p +x:u+0dzinfixed axis has a string wrapped around it as+9x02t uwzi4:d+ :anpm xf gps shown to the right. The string is pulled with a force F equal to the cylinders weight. What is the acceleration of the string?

  16.16: A uniform stick is fixed to rotate about an axis thror78f bwzm)bd8 (23f2d xdoqby6z do5xugh its center. The stick starts from f 863qyd)rz7b2 do z(mwbx5odfxb 82 drest 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 when rotating withl0r-+,qu 7j dwn;niwgbq .y. h constant angular velocity. When the angular velocqd nl7q.,uni.wbg y;r0hj+w-ity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphxbdb-,)6 3zn qdc+s mkere rolls without 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 rotational f yuq8 g5sh e4.0wu/mhinertia $0.5mr^{2}$ . 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 idea7z3beth9 uz. ml uniform ring each have mass M and radius R. Each object begins purely rolling without slimht93ebz7 z u.pping 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 0;okk:swty h3v9 dd-fand an ideal uniform ring each have mass M and radius R. Eawk:;9t hdyd03osv -f kch object begins 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 rollslyz*) -ygquy; :bnudtx0an70 without slipping on a rough inclined plane. Which one of the following choices best represents the type and directi*atl7yx gd0-yq z:)un 0nu;ybon 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 itsh-)y r*sil2lp left end. It is released from an angle θabove the horizontal. What is the magnitude of the angular acceleration of the rod about the pivot)liy2 ls-p*hr when the rod is released?

  15.46: A uniform rod of mass M and length L is fixed to rotate about a friah1; pxb u33ujctionless 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 itsa hj 3p;u31xub center of mass?

  16.50: A uniform stick of mass M a,c ih5wbds :7 y 4rv:po8vh;jznd length L is 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 stiph 7ojzd :,8 rwcbv; isy:h45vck 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 t-s0p7ma lwa4tiej( 6z hree long uniform cylinders with equal radii on the end o(4tw lsa 6i jm-z7ae0pf 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 diskw 9wb5uwj* c1os,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 mass each are mounted to rm5hb91x za yi7otate about an axis fixed through the center of the disk. Each disk is initially at bm79 x y1zhai5rest. 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 differesdtsr23ecp*4m,wa5y80a a9gvc6 ttn o d(fe5nt radii such acm ,w2g3o5*stvrd f80n(e 9adcpa4s5tet6ythat $r_x< r_y$. 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 pulz da4: 6qu7 6mnjsrct,led by a horizontal force F actincq r,z7mtj audn: 466sg
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 cloyvy ndx)):jtw:-/ob epi r+ *eckwise about its center witetev*x dw b +rj:oy/iyn-:)p)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 cylinder of mass M=2.00 kg and radiuj m5tpt z*5am7s 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 from equilibrium. When released, the cylinder rolls without slipping. What is the speed of the center of z55am*mpt j t7the cylinder when it returns to equilibrium?

  01.39: Suppose the engin49 4 v.hgsr18kixv:9tfospf re and propeller of a single engine plane are turning in a clock wise direction with respect to the pilot. The gyroscopic action of the.x kvpi1ov 8frs:f4h 4g9 tsr9 moving parts will cause the plane to move in which direction as the pilot tries to make a sharp lefthand turn.