12.43: Several forces acj ,r xw3hjs4(u5zo ou2t on a rigid body. If the resultant (net) force on the body is zero, which one of the following statemowsh 2j5j(urx34uzo, ents must be true?

  97.39: A cylinder free to turnaround a fixed,+vxq 5dvkql08ed t.intcd ) 5rb.ru. axis has a string wrapped around itit+tb dv,d55.vq)k 0qeul 8.nxdr. rc as 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 through its croil 2g 34tdb7enter. The stick starts from rest and rotates through 7b glot4r i2d3an 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 kin jglvtzld3wmmq 90 pz90x7+9d etic energy K when rotating with constant angular velocity. When the angular velocity is reduced to one-third, ttw0 9mdz9lpdjg3v+l70xq 9 mzhe kinetic energy becomes

  12.33: A solid, uniform spz8 ;dq wzy,;odvyftw895sg )yhere 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 n86.3ax q xamk,o(cv+o.ltyts.f mvj+ky 5, ehas 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 uniform ring eai47hrm*fzlzo p.u+ g7ch have mass M and radius R. Each object begins purely rolling without sliz plom7.7f zg+h*r4u ipping 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/r)-ucm o) mtc and an ideal uniform ring each have mass M and radius R. Each object begins purely rolling without slipping d-mc) r) tcu/moown 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 inclined plane. Whichm m8w* *c1.yi kvt4flg one of the following choices best fc gwk8 1t*i.4vylmm *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 left end. +n w38z qsvjq47pyu7g It is released from an angqp7vyns qj 7zw +843gule θabove the horizontal. 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 frict x8, sbda sx)xupko3 0u3+ly2uionless pivot located L/3 from one end. The rod is released from rest incrementally away from being perfectly vertical, resulting in the u3pu0xxb2,s+al)8ksu yx od3rod 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 dc5utd7 *bv /s8ibkgrru;0 0k of mass M and 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 verdrc g7*0tkudu r5v;0i b8 /bkstical, 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 ofbsro ::s keq28h:*dit three long uniform cylinders with equal radq*ebd :8ssiork: t2h :ii 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 an:;+x pylk khly j+s6+qdY, 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 t7 jwcds)wjbsw w0 983ho rotate about an axis fixed through the center 3w)wh7 bdj wsj80cw9sof the disk. 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, ha) oac 5hw;7ey:ehq2tj ve equal masses M but different radii such tha2;e5a:chot7y ehjwq ) 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 cylinder with a mass M and radius R is pul 6tffa9muz zeez91hm7*jnm9 ,led by a horizontal force F ac7z*jaen1 t m9m9zme f u6hf,9zting
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 clockwi;kni6* ekpd c/tmot zpcu.eo,6:6z4tse about its center with an angue ,z6zo 6d;n c.6ek t:c*4/tpotuki pmlar 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 sol- bf6 k;yuhl8k6d sk.zid cylinder of mass M=2.00 kg and radius R=10.0 cm is connected about an axis through the center of the cylinder to 6.6dlhu by z sfkk;8k-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 plane are9bfqx0c 3 i:4 iwuo it(s-x3ld turning 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 l4 i:xwb0 (9 udqix-l3sfot3c iefthand turn.