12.43: Several forces act on e q6gxm*mw1m0a rigid body. If the resultant (net) force on the body is zero, which one of the fogw xm*qme6m01llowing statements must be true?

  97.39: A cylinder free to turnaround a fixed axis has a string wrapped s qfot cx(f u:ap-/rog93/hp (around it as shown to the right. The ffp(oo: (tq9pr-h //ga c3 xusstring is pulled with a force F equal to the cylinders weight. What is the acceleration of the string?

  16.16: A uniform stick is fikmvabi xh/8fxl x 9(x)+o(4)8awhzcfxed to rotate about an axis through its center. The stick starts from rest and rotates througvxa48lbfim)) of8xa/kch xw(h x(z +9h 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 c,m,saw(fr:luu r )/twith constant angul,rtcr)ul,:(muf / asw ar velocity. When the angular velocity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphnsph./ .qq)zu)1 egd xere 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, )6fw4.x xeu) ussglg ,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 ic6d lvm59u54lib ;iswa+ d0zuniform ring each have mass M and radius R. Each object begins purely rolling without slipping down a roul45v b5l 9;d0wic6a mzuis di+gh 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 anteizw+w9kla0t5:)d5vw9mx7xqdeaej u) 44fd an ideal uniform ring each have mass M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. The coefficients of friction for the dilt) 5tf:9w a 5dw 90m e4kaev7exw)i+jxuqd4z sk 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 with2ifx8 kz5 ;: )dclu3yliu 6paiout slipping on a rough inclined plane. Which one of the following choices best represents the type and direction of friction (if any) acting on the cylinder as it roll;p3 l x6uzi a)ckf8:du2iy5ils up the incline?

  14.43: A long rod of length L is pivoted about its left end. It is relx:bq htmtg3 )yaer1+oz58.u ieased from an angle o1g)8iqbh 5+x3atzu. mr:tey 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 4*w goxou 1quo-uc /gp;mu o:(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 ;cx: mpooouguuq o4-( g1/w *uof the tangential acceleration of its center of mass?

  16.50: A uniform stic5x ,(f h2fmwtlwi*8y 5icx6z ck of mass M and length L is fixed to rotate about a frictionless pic zlw*c 5xi8hym wtxf,i (26f5vot 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 about the pivot?

  06.24: A person tries to balance vertically each of three long un0 n6c 1fm t21:kap*xydc bf(rqiform cylinders with equal ra*kpf0a1m x(cbn :6yc1q trf2ddii 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,i(sx9*pmp ioycnw:m8v 7 1wx* 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 rotate aond) 4+ca s5bvbout an axis fixed through the center of the disk. Each disk is initially )a+4v5 sdbn coat 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 different radii cn ;o (i1b3*4q xbia/j yrnm, s7oefj.vu10xzsuch that7x,;f oxc nmov(uij s 1qnbzrb.0a /e*3j4iy 1 $r_x< r_y$. 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 pullede 2hh6).1xu+rxee dx end q*c9 by a horizontal force F xend2xu6)c *.h1he 9 edq rxe+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 mass M and radius R r24z w71l9cj;eepxmrqeh :0p0- cpwcc px0r2dotates clockwise about its center with an angularex2cr epq4jc1-ep ;ppw7c:m xd9lr 000cz2h w 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 ha+ropk-u ga3t,q7y6 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 from equilibrium. When released, the cyl qyrp-k7uo+,g 6hat3a inder 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 u62 sh03el sk: gj3iccin 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 ssj:3ghe 26ku clic3 0tries to make a sharp lefthand turn.