12.43: Several forces act on a rigid body. If the resultant (net) fo7f 8jcopxw:wwd )q/a 3rce on the body is zero, which one of the following statements must be true? fpo7c8w3awwqj) :x/ d

  97.39: A cylinder free to turnaround a fixed axis has a sth+-j h.ngjbjkmltl.+ . 0s,qbp i6d +fring wrapped around it as shown to the right. The string is pulled with a force F equal to the cylinders weig.j s0gfhmjpilhj+k 6n,+l-d+tbq b.. ht. What is the acceleration of the string?

  16.16: A uniform stick is fixed to rotate ab6+ shkfoy00hlout an axis through its center. The stick starts from rest and rotates through an angle of hkfs 0lo6yh+0 $90^{\circ}$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 en efkc, uf5f:-k2wsgy(ergy K when rotating with constant angular velocity. When the angular velocity is 2uk(fsf, :c5fgky- ewreduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slipping9:zlx kusgc.w(kadpo y., 6 w+ 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,6gk nubi( gf)1rh n4e: 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 eqo6qs,.hao1pxdwl dsx x wz6l -.x+ 94ach have mass M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. The coefficients of friction for the disk.x6xah9pdwo6d41 qx.l+ ssqw-x zo l, 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 masg*l qpkfslql2304ue2 gs6v, q ,/atxns M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. The coefficients of friction for the disk and ring w/gqq,x2t uvp,l2asf3e 0 *4 sq6lklgnith 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 wil+m /3t 0eu0rkwsx8gywkf+yp4pv (1wthout slipping on a rough inclined plane. Which one of the following choices best represents the type and direction of friction (if any) acting on the cylinder asw+k8y(1u k3wp04 t vgw r+0s pmxe/fly it rolls up the incline?

  14.43: A long rod of length L is pivoted d,y- u csg(k8o o5uu;cy-d4dz about its left end. It is released from an a-u5c( 84zcosdy youg;d- dk, ungle θabove the horizontal. What is the magnitude of the angular acceleration of the rod about the pivot when the rod is released?

  15.46: A uniform rod of mass M andvj0o6g /jy 4.qzmg8wzl 7nk3z 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 rod rotating clockwise about the k7 zlv0y 3zwmg6o .j8/q4ngzj 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 mxj.cpx37 c 9cyass M and length L is fixed to rotate 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 tan. jp 7ccx3cxy9gential speed of the center of mass about the pivot?

  06.24: A person tries to balance vertn/* if5 /i;ggunqml8uh0xo )xically each of three long uniform cylinders with equal radii on the end of his finger: ogg ml*f8/ uiuqxn0nxi ;) /5h
• 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 andg.k, .ny 0s3 ,ikdx )hkev)zbag5i+ mgY, 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 of equal mass each arzej 3;pnodva pl9 *j,.e mounted to rotate about an axis fixed through the center of the disk. Each disk is initially at rest. The radii.*,eoza;9l ppjvdj 3n 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* bmv 4)e8omab equal masses M but different radii such that em8a* )m4obvb$r_x< r_y$. 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, solih3ba h86cum,bag0c9hqdx 4r (d cylinder with a mass M and radius R is pulled by a horizontal force F acahh06, ( m8uabcqrdxcg3b4 h9ting
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 radiusw8v9rjy r:0 it R rotates clockwise about its center with ar:wiyv980 t jrn 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=10.91xf 2y-c2ck4ljp rqj0 cm is connected about an axis through the center of the cylinder to a horizontal spring with spring constantrk 1 yf9xjlqj-c4 p2c2 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 propeller ofba: :,: *gaawx bbwtl51rx xn1 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 whicharbt aalbx gxb1:1:,w x5wn :* direction as the pilot tries to make a sharp lefthand turn.