12.43: Several forces act o;jbds8ud5 xs. wt8b,t n a rigid body. If the resultant (net) force on the body is zero, which one ofb85xsj w,8;tdb std. u the following statements must be true?

  97.39: A cylinder free to turnaround a f(7p za;s jrme7ixed axis has a string wrapped around it as shown to the right. The string is pulled with a force F equal to the cylinders weight. What is thzams7 ep( rj7;e acceleration of the string?

  16.16: A uniform stick is fixed te/qnv-e)9o rd )c0pi3 6adsde o rotate about an axis through its center. The stick starts rd v)-id9)n/6peeeq3dcos0a 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 kinetic +lhsarnxv43brb3h )m:* s3o a energy K when rotating with constant angular velocity. When the as3)h b:nr3s oaa3 4hmr *v+bxlngular velocity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere eufwx11 to11crolls without slipping 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 rotatioki ;oy 2f,p7hunal 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 unifor)hz;z,qa,2fk-qw dr bm solid disk and an ideal uniform ring each have mass M and radius R. Each object begins purely rolling without slippinga2kbd)r zwz,q;f- q,h 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 rinji,d ncl-e68 x;s lq v:14xlheg each have mass M and rh,6:1x4 8illn-j q x;lsedcveadius R. Each object begins purely 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 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 bl s8vx+m vpi(5ise9d u1p:g( on a rough inclined plane. Which one of the following choices best represes(p vvgi s(e9mx+1d:iupl8b5nts 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 Le*6fy ,9 cpgi2.kgqcx is pivoted about its left end. It is released from an angle θabove the horizontal. What is the magnitude of the angular acceleration of the xce2 ipg6*qc9fk. gy, rod about the pivot when the rod is released?

  15.46: A uniform rod of mass M and length L is fixeel;s- 0 tzag f)/fcja/d to rotate about a frictionless pivot located L/3 from one end. Th)flf/z-t;ej / gcas a0e 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 fixed to rp4e* vdam9*zoa6e09 alxt rs5otate about 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 speed of the center of mass ab6rs zdm e9a0t54xl*vao* e9ap out the pivot?

  06.24: A person tries to balancjo 3l avg -cjtx,hs9,78qc2g de vertically each of three long uniform cylinders with equal 9 sqchtc72 g3,jolgd x-v8ja,radii 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 din 6)ghv;( nv (dbzj dm1:rj-jvsks,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 unifo0/stg4sor(q:i no++ l3des4f p rbtl:9p0e tzrm disks of equal mass each are mounted to rotate about an axis fixns l::ssotb(qlt/e+g+3 0f49e0odr tr 4 zppi ed 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 masrqnr nn .)w+q)ses M but different radii such thatn)rnw+qn. qr ) $r_x< r_y$. 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 cylin n a6r;/co:96x kqag,k rnsu2mder with a mass M and radius R is pulled by a horizo s2:kumrx;o6 6/r agcn9 aknq,ntal 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 d g6bf:wreu+n( isk of mass M and radius R rotates clockwise about its center with an angular speewf6u:e+bn r( gd $ω_0$ . 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 r2a*t o0 r/+qkcj a. :uznae+edwbzz- b*4s z.radius R=10.0 cm is connected about an axis through the a -e0b*je .s+qw bc*nua+ k. 2zz d:rorztza4/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 prxx(7 w)oxpaeud(8 h6jjibq+ ) opeller 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 direction as the pilot tries to make a sharp lefthand tx+e)6j7ahx jpw bx)8(qu( oid urn.