12.43: Several forces act on a rigid bodhb) k te2 yy0 6eh72f9a3ava,*hqakfpy. If the resultant (net) force on the body is zero, which one of the followa7 22 fqhfyh3bek*,y 9)aahk vea 6t0ping statements must be true?

  97.39: A cylinder free to turnaround a fuufg5wugi e l-m8-qo.dg-/p6ixed axis has a string wrapped around it as shown to the right. The string is pulled with a force F equal to the cylinders weighwep-q 8m/ -l fu.oiug6ug -g5dt. What is the acceleration of the string?

  16.16: A uniform stick :a cx/wxlsr36*hcm)4r ,ilkpis fixed to rotate about an axis through its center. The stick starts from rest and rotatesxi,:hx)s l*wrpr43 c/ kla6m c 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(rkuvnra)k3pv241wu 3f( tzs kinetic energy K when rotating with constant angular velocity. When the angular velocity is reduced to one-third, the pk )vztf( ua(usrk4n3231 wrv kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slipping ongo7 9o/ut xv;3wvptv.p,ryi2 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 mass2 1 zw )tmd)kap+bz dy95betp; 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 uni6w rl:8yt 1qzsform 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 disk and ring with thtql1:s 8w6yrz e 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 unifo7hcoyl 0a9 ld yf2+sw*rm solid disk and 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 frictiw*0ll dosy 9y7ha 2+fcon 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 rf3 9duyb ww ir9,k 6gxs;ul.t(-r *j-u:qgpriolls without 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 y.lw*iu- purs;3(w u r9 r9,dfg-kqt6:jbixgas it rolls up the incline?

  14.43: A long rod of length L is pivoted about its left end. It is released zkhp1i4eodywy8 uk6:4*, g gbfrom an angle θabove the horizontal. What is the magnitude of the angular acceleration of the rod about the pivot whe,zbyyd *g 6wopk 4g ekhu4i81:n the rod is released?

  15.46: A uniform rod of mass M and length L is fixedccz. d d;3mk+g to rotate about a frictionless piv+ .c 3;dcdgmkzot 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 mass?

  16.50: A uniform stick of mass M and length L is )wtdfh 76:x(1jch yegfixed to rotate about a frictionless pivot located L/3 from one end. The stick is r6)(fdhhwj cget: 1x7y eleased 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 uniform cycnl2 f2wk;n2gm;ho; plinders with equal radiln;2h n gp;2om;cfk2wi 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 ma/ uw8w5qd;byxl64r hnsses $m_x$<$m_y$, 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 ar6xvj k,a-p3j(lg fh)a e mounted to rotate about an axis fixed through the center of the disk. Each disk is initiv6xaj - h 3jf()kp,algally 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 an svult*tgvk1b.i0v77d kks4y: 8gu 7t yng3n+d Y, have equal masses M but different radii such kn3. 4b0tgsy7v u8:i7n7dt*l ygu1vkvs+ g tkthat $r_x< r_y$. 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, solioc6m:tx5 f6uq3x-v) ;lv e vpwd cylinder with a mass M and radius R is pulled by a horizont mvf e5vq;l t-vxcx:o)6u6w p3al force 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 mass M and hal ):.y zup.k( (cqqgradius R rotates clockwise about its center withyz . qk)lu(:qgh(a .pc 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 Mfw/kg isahs.ea)24k* =2.00 kg and radius R=10.0 cm is connected about an axis thr. kf/i ewkas a)42g*shough 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 the cylinder when it returns to equilibrium?

  01.39: Suppose the engine and propellesnskfzm7j; z50kj * u3r of a single engine plane are turning in 7;s 0smjn5j*k 3f kzzua 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 turn.