12.43: Several forces act on a rigid body. In8( 9p *aeivlyh06hn of the resultant (net) force on the body is zero, which one av*6he98 0ph ln(oyi nof the following statements must be true?

  97.39: A cylinder free to 3omay( z ubro9,rgkm : 3u2y3 f,q)ndzturnaround a fixed axis has a string wrapped around it as shown to the right. The string is pulled with a force F equal to tkamqzofo z(3)u3rm ugb nd,9, yy: 3r2he cylinders weight. What is the acceleration of the string?

  16.16: A uniform stick is fixed to rotate about an axis through its8tnn4;ef+:8fxizr z yp ibp(- center. The stick starts from rest and rotates through an aypt+4e8nn ;fiz 8px b f(r-:izngle 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 aqmg3(j 8ymrqlhwo; (g1 /s*b rotating with constant angular velocity. When the angular velocity is reduced to one-third, the kiner oqyha*1b83m/g(gj;qsm(w l tic energy becomes

  12.33: A solid, uniform sphere rolls without slipping on a floor along t sv.8b -rp cl;eo,x/hwhe $+x-axis$ (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 masso dns6/ ;p 7du,ilsetnm1r.y 3(o4y bk 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 have mas/wqws:ex;t ) 9di x5qhs M and radius R. Each object begins pure;9q:xe siwx)qwt h5 /dly rolling 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 idea91spbfw c j/w7l uniform ring each have mass M and radius R. Each object begins purely rolling without slipping down a 7fc swp9/jb1 wrough inclined 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 slipping on a63dw 2go)ow hlk6skk ma5id 88 rough inclined plane. Which one of the following choices bsmk8d5w6 a2k3o 8ogk)lih6w dest 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 tfv r ne6 yu5h8++ 9qoeu0ff5rL is pivoted about its left end. It is released from an angle θabove the horizontal. What is the magnitude of the angular acceleration of thtnu +e rvy 5rufofqf+8e60h95e rod about the pivot when the rod is released?

  15.46: A uniform rod of mass eh,6dym2mdu 9o1 aei .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, resulting in the.6mhda e emi12yu, o9d 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 lengthr;s5zz hbu a ri/d:5x, L is fixed to rotate about a frictionless pivot located L/3 from one end. The stick is r55h:zzd xruas ,rib; /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 trieqa :-/ew9sc 9 :kllggbm*dmm /s to balance vertically each of three long uniform cylinders with equal radii on the d9/c:mb-w aklg/mes:mql 9g* 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 disk4 ssbrzj85 y /ny;wzu1s,X andY, 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 8rklw(3tcfip5ap wkb5 05h6n w tk 4pbn-.w 7fof equal mass each are mounted to rotate about an axis fixef-55c.p8(r wpik7w w50t n6p4n kb 3fkbhlat wd through the center of the disk. 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 equal masses M but differ8g gq0pn7)bdv +rs- nhent radii such that p0h gb rdgq7+sn)v8 n-$r_x< r_y$. 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 ze 2w) )cgrlp :t/6wjtM and radius R is pulled by a horizontal force F a) ) wgpzt6re/ltw j2:ccting
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 anuem ycr3f9,dwdu ;+rt5 .gwg.d radius R rotates clockwise about its center witheu9 35,rgm .t;cw +fg.dwr ydu 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 anxyg 8i1 dy .+0prh9k.jo3ihm kd 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 cylinder rolls without slipping. What irg1 ox30 kjmip8diyk .y+.hh9 s the speed of the center of the cylinder when it returns to equilibrium?

  01.39: Suppose the engine ae 7.k,mmn+t2j tz bgv4nd propeller of a single engine plane are turning in a clock wise direction with respect to the pilot. The gyroscopic action of the moving parts we 7mnmtj gb4z.2 +t,kvill cause the plane to move in which direction as the pilot tries to make a sharp lefthand turn.