12.43: Several forces act oey 2b./xdl0uv,s h(o ko, :qkvljh( 8zn a rigid body. If the resultant (net) force on the body is zero, which one of 8sk v lhq0 loy,kvh.,/uj2:e(dxzbo (the following statements must be true?

  97.39: A cylinder free to turnarounm80jcg+s 4zjetks7t/ d a fixed axis has a string wrapped around it as shown to the right. The string is pulled with a force F equal to the cylindersj4j kzgs+ 8 t7s0e/tcm weight. What is the acceleration of the string?

  16.16: A uniform stick is fixed to rotate about an axis through its cen.k0) c 63ojwkklbdz4zter. The stick st wzcd)3lobz k6jk.4k0arts 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 enercs;7;wkovg x4 gy K when rotating with constant angular velocity. When t7x;oc ;k4 gvwshe angular velocity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slipping on a fl ku *w(2f,bohl bb/s1toor 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 rotae)n5xwf o ,)szh :)ak /xmi;a8mj+ul3txwk a 6tional 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 /j (9ubg7rrb ysolid disk and an 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 fr(ry7 9jbrg ub/iction 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 unifc4d- 9nb4:t br; mmcwform ring each have mass M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. The coefficientsbt4nrm;:m c fbcw 49d- 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 a rough inclined plane. Whi (v2cziqp*z 8btd fk)f :r9o,hch one of the following choices best represents the type and direction of friction (if any) acting on the cylinder as it rolls up thehd b,k2fv9 )(:qzr8zpofct *i incline?

  14.43: A long rod of length L is sek 51gbfzy +62 lm0-4rzdgqkpivoted about its left end. It is released from an angle θabove the horizontal.46l+2r z1s0gk-qgd k5ebmyf z 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 fr ux8 3u+ucdnn.ictionless 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 pivon+n x .u3cudu8t. 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 rotate about a fricti*f pi7:d ym6fnonless pivot located L/3 from one end. The stick is released from rest incrementally away from being perfeci7ydf: n6 mpf*tly 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 vertically e1s gnyrn ht1h l-pgqhe2 l-3dl,q 19+nach of three long uniform cylinders 1h-glhe,n- q+y19 q1tlgnlp shd32rnwith equal 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 disks,X andY, have masses td(y f k*dxb/,$m_x$<$m_y$, 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 aiw w4p/zdp74cre mounted to rotate about an axis fixed through the center of the disk.7piw 4c/ dwz4p 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 different rbfa1- dwd64q cadii such that 1fbq cw-d64 da$r_x< r_y$. 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 M and mg7u+fh y(kw* radius R is pulled by a horizontal force F achmu*w7(k fy+g ting
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 radiuf0x qcr)c* h6byv 1nz2s R rotates clockwise about its qz*y c2cxr0v)b 6n1hfcenter with 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 a chl d.k:m xml-t;9q+tnd radius R=10.0 cm is connectet t-lxqdm hmc9k:.l+ ;d 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 equilibrium?

  01.39: Suppose the engine and pr-n/arfyrqif7se8 7 l m. ds.;7din4b dopeller 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 sharnr7 .id7i4d8 e/-flqsb ay.dsfn7 ;mrp lefthand turn.