12.43: Several forces act on a rigid body. If the resultant (net) force on the ww.vgl4 lgujlyqg0t/ o0 2.(qbody is zero, which one of the following staov.y 4q glwwgtqg. ll(0u /02jtements must be true?

  97.39: A cylinder free to turnaround a fixed axis has a stb oow8ls6t q xzcp6u .2ou2v*;htg7-lring wrapped around it as shown to the right. The string is pulled with a force F equal to the cylinders weulvbuts.- h ; t6z2 og7*6o pqxwl28ocight. What is the acceleration of the string?

  16.16: A uniform stick is fixed to rotate about an axis throu kyj /cqit2-f53ie9 hjgh its center. The stick starts from restecfjyji 92/t-qk53ih 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 with cons6 ot.p ;aqw8butant angular velocity. When the angular velocity is reduced to oneo p. a6bwq;8tu-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without sligfn7g/a wp8 mtw-l1 jus+6z 85,zh meepping 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 inerti3y cdvun ;x3tiisk sh1kpi f7 +yw72)2a $0.5mr^{2}$ . 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 i6;s kjjn4;btz,dnbm0w9ay2 g deal 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 t;n4b, 2gjsa6kbwjm tn09d zy;he 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 and an ideal uniform ring each have mass M and)dh0p2 sjtxp (7kyvrs;+a;i i radius R. Each object begins purely rolling without slipping down a rough inclined plane. The coefficients of fip +;ys(d0 )h7irskjp; v2xatriction 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 zfik a0lml.30u5s.e rprw 6 k:on a rough inclined plane. Which one of the following choices best represents the ty u.k0a 6sml er0:p.3k5ilzwfrpe 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 abouqq v) fl;quo)( zue2m8jp,(uyt its left end. It is released from an angle θabove the horizontal. What is the ma);lze8vymq q,uquup(fo)2j (gnitude 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 frictionl3bn6fji0vbl+vs 7 9ewess 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 6b0 +ivl7fw e3n9jvb sof the tangential acceleration of its center of mass?

  16.50: A uniform stick of mass M and length L is fixed tovhcm/1fqxl 8g,(r) 2 a ve1vy.g. epgy rotate about a frictionless pivot located L/3 from one end. The stick is released from rest incremhggma,lqepf21 /).re y vv 8 1y.xcvg(entally 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 l;8:qr3r t nukctzum2lav) 6-vertically each of three long uniform cylinders with equal radi;ut :)lla3tr cnruv-q8k 62zmi 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 massi1a rs e luabu( 0ykk(8sw7v66es $m_x$<$m_y$, 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 diskk/pmeb. .1fwv s of equal mass each are mounted to rotate about an axis fixed through the center of the dme v./.w1p bkfisk. 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, have eq6d2dg d0 ivl8vual masses M but different radii such tha0gd68didvl v2t $r_x< r_y$. 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 rad / bexzsd bq,i9 dsxnr*0(-f;oius R is pulled by a horizontal force F-b/q0 x,dz9 xs eisfo *rn(b;d 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 a6t.t tm*lr zy.nd radius R rotates clockwise about its cetzl.mt. y r6t*nter with 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 radius a7:3v gsi po/tR=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 the cylinder: iapg3ots/v7 when it returns to equilibrium?

  01.39: Suppose the engine and propeller of a single engine plw-t+kt g 8dhf 1kxf70yane are turning in a clock wise direction kxg01t8fy-tfkd+ w h7with 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.