12.43: Several forces actx3)6ikyhj;ec8 . ozun on a rigid body. If the resultant (net) force on the body is zero, which one ofzu3yj.6k )i8 ;on cexh the following statements must be true?

  97.39: A cylinder free h o ie(*odulzph4w8a3k3 )v( .3aejxito turnaround a fixed axis has a string wrapped around it as shown to the right. The string is pulled with a o(hieaalu .z(kx433we )p iojv*8h3dforce F equal to the cylinders weight. What is the acceleration of the string?

  16.16: A uniform stick is fixed to rotate about 5 )f2 r* pi:u evohh7iaf2dq8han axis through its center. The stick s eahrqf)7iufih8d2:h vp5 o* 2tarts from rest 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 ki0huwz i0ei-b .netic energy K when rotating with constant angular velocity. When the angular veloce u.h-0bii0w zity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without ;xhu9 ss+c8zaslipping 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 maphzut p91jyz),qavhv.9u 6 7zss 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 each hkyezgo:v7) s1 ave mass M and radius R. Each object begins purely ro:71 sgye vk)zolling 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 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 h)32rc /cj hoquave 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 ri cq2 j/h3o)rcung 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. by 7i 8bem5/b:h daai3.kwjk:Which one of the folloiyhkbb/5 .m::ajidwaeb k387 wing choices best 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. uc dp2uogte; j.a*2 y,It is released from an angle θabove the horizontal. What is the magnitude of the angular acceleration of the rod about the pivot when the jt acg,uy2uoped2*.; rod is released?

  15.46: A uniform rod of mass M and length L is fixed t,o:: nj;lytr:vhedy/ px+u0 xo 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 c /0jut:r;lod y:xpv:,xn +ye hlockwise 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 fixed to rotate about a w;;uen3h q*pyyj/ 7m ofrictionless pivot located L/3 from one end. The stick is released from rest incrementally away from being perfectly vertical, resulting in the 3 ohjw;y/yu nep7;*qmstick 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 cylin):9jd iohowy4 ders with equal w 4)h:ooi9dyjradii 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, havr m;8gi4 (ihggw+j +cqe 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 ro+q2kx bkluh6ul6* e:s tate about an axis fixed through the center of the disk. Each disk is initially at rest. The radii of the disks aqlkxl6bs*e6h +: 2u kure $r_1 < r_2$. 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 eb :,pw.;mvoakqual masses M but different radii such that;. oak p:mvwb, $r_x< r_y$. 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 andebz-bn.i/ 9 l+ ysjxr9 radius R is pulled by a horizontal fin xe -s9z/yj.9+ bbrlorce 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 M00(p yv (zut,)pz(bm 0*cpbgqyk9mkgfr4; l a and radius R rotates clockwise about its center with an a, p9gbzaktpqr(;(b0(l0my)k fgpzv0 * umcy 4ngular 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 R=10.0 cm is con dgs0,snoycn i./ w;(t(rm0bousno)(nected about an axis through the center of the cywusnotdcr0n b( gssom)i(y,o ;(.n0/ linder 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 prg 9k, 4dojn.n z/sea+vopeller of a single engine plane are 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 direct4g+ sn9ka/vzdn, e.ojion as the pilot tries to make a sharp lefthand turn.