12.43: Several forces act on a rigid body. If the rp2 twjo b0deh*x( ptz8f j1 j5l+s+j:tesultant (net) force on the body is zerht(epp wb 2jxj+l0tst5f 8d* + zo:1jjo, which one of the following statements must be true?

  97.39: A cylinder free to turnaround a fixed axis has a string wrapped aromlct zhj)7ie +7d 3nwfh )0/pqund it as shown to the right. The string is pulled with a force F equal to the cylinders weight. What is the h e7i0jd)cn 73/zmpql +fh)twacceleration of the string?

  16.16: A uniform stick is fixed to rotate about an axis through its cen ,-2fay wuva6ster. The stick starts from rest and rotates through an angs2vf awy- ua,6le 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 h g2* r dm5g9oqvb1p)icas kinetic energy K when rotating with constant angular velocity. When the angular velocity is reducedg1o*pbvrq d5) migc 29 to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slipping on a floor ao*pzr 7r0 y,a0v;huq wlong 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 rotatiiy 2 -jxb8gx9un:g 7oyu6+acjonal 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 andp; 9 er afb 1(+h yesh(qblf,96hqwtp( an ideal uniform ring each have mass M and radius R. Each object begins purely rolling without slipping down a ro,l ph16aw(eybq9 t+fsh(eh9( fpq;rb ugh 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 d zo9rsec.h, .rturaz)w. rd2 ;.bv2 flisk and an ideal uniform ring each have mass M and radius R. Each object begins purely rolling without slipping down a rough inclf.. e crauwbz 2ltrr,.. h)zr9dv; os2ined 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 slipq.-k2zequ ywlkpom2w/( .dyp+ ,ju8pping on a rough inclined plane. Which one of the following choices best represents the type and direco.qp2. wp u+/q yjym,e-8w(lzd k2uk ption 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. It is,l; ) yphwatk: released from an angle θabove the horizontal. What is thk,lyptw); ha: e magnitude of the angular acceleration of the rod about the pivot when the rod is released?

  15.46: A uniform rod of mass*x1/atnewlfgb6 b8 e4 M and length L is fixed to rotate about a frictionless pivot located L/3 from one end. The rod is released from rest incrementally away from being perfectly vertical, resulef4b te81n/x bw la*6gting 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 fixed to rotate about:6dmghol;h bwiaa v;104n s(g a frictionless pivot 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 spee;o 4hadvbhg na; 6:0(ismw1lgd of the center of mass about the pivot?

  06.24: A person tries to balance verticalj da/v:gzp+u-ly each of three long uniform cylinders with equal ra:+ d-z/auvjpgdii 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, hah go22lsin-e- ve 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 y )skfvcf.(j)2k)xal rotate about an axis fixed through the center of the disk. Each disk is initially at rest. The radii o2afkf cyv) (l)sxkj.) f 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 s.sfv v*is*ok:x; 0yiradii such t v*vf:xyissisok.;0 *hat $r_x< r_y$. 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...fdj9(8y ncdaqpl bius R is pulled by a horizontal force F ac 89byclj (nd.a. .qfpdting
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 rot0 zz;+7 ervmn)6kv yalates clockwise about its center wl;6mny+7 k zv zvea0r)ith 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 R=10.0cnz)r: ez .l,rfe 0cu8 cm is connected about an axis through the center o cnfru,)z 0c8z.l :eref 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 eng fts7791* hx/difwgyqine and propeller of a single engine plane are turning in a clock wise direction with respect to the pilot. The gyros qdygwf/xih19f7s t*7 copic action of the moving parts will cause the plane to move in which direction as the pilot tries to make a sharp lefthand turn.