12.43: Several forces act onw dartq;:of(e xm6*f) a rigid body. If the resultant (net) force on the body is zer wxre; f6*f)dmoqat:( o, which one of the following statements must be true?

  97.39: A cylinder free to turnaround a fixed axis has ():voru)n0ayq l3auyta tt9, a string wrapped around it as shown to the right. The string is pulled with a force F equal ton(yt ua r0at at, :oqyl9)u)v3 the cylinders weight. What is the acceleration of the string?

  16.16: A uniform stick is fixed to rotate about an axis through iv)w09y ipmdtua2: irl.2rsi 1ts center. The stick starts from rest anm2t 9a0 sv.1 :dr)luw ri2iiypd 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 kik ub6m vw1rv gb3(tb88netic energy K when rotating with constant angular velocity. When the angular velocity is reduced to one-third, the ki( bk mb88vv3gr1w utb6netic energy becomes

  12.33: A solid, uniform sphere rolls without slipping on a floor along ji bvpw/7tf 3z 0,d,wqthe $+x-axis$ (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 -o/ib av6l(t nb+z0 frr, 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 ea+ uqij 3b5ldn9qo1 c)dch have mass M and radius R. Eal u9d1q cjo)3+qd5i bnch 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 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 x 2v(b/6f30pccu lggcan ideal uniform ring each 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 and ring with the incline a6vbgc0x/fc2(gpu 3 lc re $μ_disk> μ_ring$.
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 rmb;7irb2znw81xsumnlaxo, +1s b r1153x svq olls without 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 cylinde7xm 1s+bbax3 uw zxr5i r,s11nbl21omn svq; 8r as it rolls up the incline?

  14.43: A long rod of length L is p(xfwvira 4r */ivoted about its left end. It is released from an angle wv(i a/4xf*r rθabove 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 and length L is fixed to rotate about a frictink* gzz81/o qpvheqe 6j:0zkg5k: a kpku332vonless pivot located L/3 from one end. The rod is released from rest increm 6 g zq: oj vpqz/kazkp 3*vn1e2:0hk5ekk8ug3entally 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 mccg7kf vi27 +mass M and length L is fixed to rotate about a frictionless pivot located L/3 from one end. 7fmcvgi7+2ckThe 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 about the pivot?

  06.24: A person tries to balance verti b)2b x;v;rkyycally each of three long uniform cylinders with equal radii oy;y)vr;xbbk 2n 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, have massesb0qrsxy: v h .5+id zyp/qvai 3e)c:;g $m_x$<$m_y$, 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 76evwt *jp2jrrotate about an axis fixed th 26vwp*jt7jerrough 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 oabm;wt.kpdkvr6d08 2g 55c p, X and Y, have equal masses M but different radii such dca5k povrg db; p86w.t250kmthat $r_x< r_y$. 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, somgdm2 ekvp-0;lid cylinder with a mass M and radius R is pulled by a horizontal force F acting 2 g;0v -mdekmp
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 11cj rjd6 ju 2ig*3kdkM and radius R rotates clockwise about its center with an angular speed6jkcu21r1dd 3jj*ikg $ω_0$ . 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 is4,eiv p)n3 vuu 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 is the speed of the center of the cylinder when it returns to equilibriu4 ,euvnpv3iu) m?

  01.39: Suppose the e:d qvf8-(g4x hcrku7kngine and propeller of a single engine plane are turning in a clock wise direction w(:8 7vrk4h-u dgqxc fkith 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 turn.