12.43: Several forces act on a rigid body. If the resultant (net) force on upm 7xbsi3rc q0fg7 2m o;ce48the body is zero, which one of the following statements must be true?qc0s2 m8co u77e3pb; m fgi4rx

  97.39: A cylinder free to turnaround a fixed axis has a s0ov0ah p ua12tz+hfm/tring wrapped around it as shown to the right. The string is pulled with a forc1 fv00hapot/ az+2uhme F equal to the cylinders weight. What is the acceleration of the string?

  16.16: A uniform stick is fixed to rotate about an axidd*kvz6 *opt:v*snk ((jkzwdhp 35*hs through its center. The stick starts from rest 3zwn kk*z t:v 5d(pv*6(*s* kodhphdj 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 energy K when rotating with cona z,mdo*v*u5nf64g cw stant angular velocity. When the angulaz *vnda6c,m5f *wguo4r velocity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without s .1stzg+j5 l)t3tcxnulipping 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 rotation:0/nw g zk jpi56nre,94nbp3vqd 3ycwal 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 disw*q5s; x8v g tqu;,fagk and an ideal uniform ring each have mass M and radius R. Each object begins purely rolling without slipping down a*;t8qxsw fgug;vq a5, 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 anen447v w-d6ypfsp 6gt d an ideal uniform ring each have mass M and radius R. Each object begins purely rolling wi4sfv746pp -dyegw6tn thout 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 r4qw1 sj(rg c:jolls 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 cylinder as it roll14:jr jqg c(wss up the incline?

  14.43: A long rod of length L is pivoted about its left end. ululn7*;s (51l;mbuclhipy r:) x sj 0It is released from an angle θabove the horizontal. What is the magnitude of the angular acceleration of the rod about the pivot when the rod is releu si5h lx)* lu y7r(j;c0 bp:l1lmus;nased?

  15.46: A uniform rod of mo(,9zgd3s 4zdo9j xwoass M and length L is fixed to rotate about a frictionless pivot located L/3 from one end. The rod is released from rest incrementally oo(w9 sj3oz zxgd4,d9 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 madqgjz z ,i7k)7ss M and length L is fixed to rotate about a frictionless pivot located L/3 from one end. T,kzgz)i7 dj7 qhe 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 vertically each of three long uniform ./q;gvu+pojc8xb 5/ffo9 ya;.aa mxu cylinders with u5x;b8 g;/vpo oqc fy9+ufj.ma.a/ xaequal 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,/ 1;pq47-fr sg emjdqr 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 e3 y (oo (3ehznkjt70n ;dbja-yqual mass each are mounted to rotate about an axis fixed through the center of the disk. Each disk is initially at re3dtby(k- nao0 jjny7(eh o3z ;st. 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 equn-aatb(4w8b ual masses M but different radii such tt(-a aun8 bw4bhat $r_x< r_y$. 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 cjrplc/4r 0p ;7 j-iafpylinder with a mass M and radius R is pulled by a horizontal force cl;r0r7fj p-/ip 4jpaF 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 y 7x//n,s70bri ilmlyisk of mass M and radius R rotates clockwise about its center with an anguyi 7bn/li, l s0xy/r7mlar 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=10.0 cm is conne d-a2vawtq0)a;cl 7ooa4*ficcted about an axis through the center of the cylinder to a horizontal -0a*4f coavc);dai2t7lq oawspring 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 prt u-qhw4y 6zfi2;*he iopeller of a single engine plane are turning in a clock wise direction with respect to the pilot. The gyi6tuizhy 2* ;whfq-e4roscopic action of the moving parts will cause the plane to move in which direction as the pilot tries to make a sharp lefthand turn.