12.43: Several forces act on a rigid body. If the resultant (net)baw/ zk nal/qst(e h/:*v*wf 8 force on the bow/l**:aqszhf bvk(/ae/8tn wdy is zero, which one of the following statements must be true?

  97.39: A cylinder free to turnarok*co2niuv ; x/und a fixed axis has a string wrapped around it as shown to the right. The st ik/ouc;x nv*2ring is pulled with a force F equal to the cylinders weight. What is the acceleration of the string?

  16.16: A uniform stick is fixed to rotate about an axis through its center.9et(fmh w;brntqi)3c. da z +) The stick starts from rest and rotatesf9wqi+ cr)nez3b ah.(;ttmd) 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 energy K when rotatinph ea+m:z; +si ujb+g8,umy8fg with constant angular velocity. When the angularzmjua+e8m,uyp b sg++; fhi8 : velocity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls withob+b:s7 pmon 0nvv6l9t puaj,j3sc4:p7bj4jv ut 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 rotational inerti d2t uo..o b9zuheu/)va $0.5mr^{2}$ . 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 mass M anv-o3z 7els7-s s gs9pcd radius R. Each object begins purely rolling without slipping down a rough inclined plane. The coefficients of friction for the cs3zv97-po -s 7esls gdisk 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 uni z cu38g.da 2vc:b+9cytffax1rec 61bform 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 with28ab.rf u6 fx t91ca:d gce13 yzc+bvc 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 withoybf;jw 3n)ks,ut slipping on a rough inclined plane. Which one of the following choices best re,js;byfw3) knpresents 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 Lx z 38qk2z+hhj is pivoted about its left end. It is released from an angle θabove the horizontal. What is the magnitude of the angula jz xk3q+hzh82r acceleration of the rod about the pivot when the rod is released?

  15.46: A uniform rod of mass M and length L y;* g,dtv 2(gryr9 gpgis fixed to rotate about a frictionless pivot locatedg* d, ggyg9rp;y2vt(r 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 pivot. When the rod is horizontal, what is the magnitude of the tangential acceleration of its center of mass?

  16.50: A uniform sticke9*ttm.q v1n c of mass 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 tangential speed of the center of mas 1*tc9mvnte. qs about the pivot?

  06.24: A person tries to balance verticalu(mtn4 wce:j+4 y53jzqt ugc 5ly each of three long uniform cylinders with equal radii on the end of his zq 4:5(jmc c 4yu5uwj+eng3ttfinger:
• 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 massebt/j tc sk /p66,truuww4, f1es $m_x$<$m_y$, 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 du/a xna*:d7 7uev le1:ljt0vqu*6d lmounted to rotate about an axis fixed through the center of the disk. Each disk is initially at rest. The radii of thlduxtlq n7*0d 7u6udjeve:v/ l1 a* :ae 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 dy,ql fk3 ;oki4ifferent radii such tha4kqi, yfk ;3lot $r_x< r_y$. 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 cylijd24hig ,dh5under with a mass M and radius R is pulled by a horizontal force F acting,h5hd 2dguji4
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 rotates clockwise abouty7j )ttga7ib l).1pkn its center with an angular sapn ) bk.71tgi)7tjylpeed $ω_0$ . 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 sol59l, zk a;mjmnid cylinder of mass M=2.00 kg and 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 is ;k5ajmm9ln ,z the speed of the center of the cylinder when it returns to equilibrium?

  01.39: Suppose the engine and propeller of a single engine plane are turning infvfs38is 8 m,y 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 m8 fyi, vs3m8sfake a sharp lefthand turn.