12.43: Several forces act on a rigid body. If the resultant (net) forca:o-;u ox.k(/vdfzga e on the body is zero, which one of the following statements must be trueoa -ku/o (dx.vz a;gf:?

  97.39: A cylinder freyyi,+ zsh .mi4-jdc(l e to turnaround 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 cylinders weight. What is the acceleration of the .jh(idy-s,4+c ziylmstring?

  16.16: A uniform stick isq5o6odvwh8 (/r h+ xnc fixed to rotate about an axis through its center. The stick starts from rdr8qv5 w hx/+6(hncoo est 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 rota+ w5og1b 7 ;7i(9hnwb6e o;dbelznzxo,)wxnqting with constant angular velocity. When the angular velocity is reducein+ x5 n)db6lobe,ho 9 wwb qx7(wz o71;zng;ed to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slipping on a floow1 lc (5wv5bxer 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 maj1/(uek3p i jhkbm8o;ss m, 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 unifor+d7o lk1z gvv3m solid disk and an ideal uniform ring each have mass M and radius R. Each ob7 zvkgdl+3o v1ject 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 an ideal uniform ring each have mass ;n2 h-ifz gxg68fxowv u3 xp;(l cfpmo6v6p7:M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. The coefficients of fr fmh p6co;x8gpl76opv: ix gxu(ff;-6 nz3wv2iction 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 inclbqe5t q.gj72 nined plane. Which one of the following choices best represents the type and direction of friction (if any) acting on the cylinder as it rolls up the incl2.bq7etqjng 5 ine?

  14.43: A long rod of length L is pivoted about its left end. 8pmfb61y q 6k6+2l;rqajqrsh y woz-+It 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 re8wb k;2yz1q+6 rqqlmay +jr- fps6ho6leased?

  15.46: A uniform rod of mass M and length L is fixed tolp5 ; fn1;e*z0tifjk a rotate about a frictionless pivot located L/3 from one end. The rod is released from rest incrementally away from being perfectly vertica tie 5f0;pjf;zn1k* all, 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 mass M and length L is fixed to rotate about a f*4o97 .kfvtcf6 y:ihqbc q it.rictionless pivot located L/3 from one end. The stick is released from rest incrementally away from being perfectly vertical, resulting in 9.v:qcchq6f.tof ib t4i*7y k 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 eac9 )f(-eyp;pnvnoyr,dwe: k - jh of three long uniform cylinders with equal k-nf p 9e(dvynyj;,wepo:)r- 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,czdn urkdn+evv c:3/zknc2 u/2) c9/cX andY, 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 e 8ayy1uci/)jj.tba9pfdo/4 lqual mass each are mounted to rotate about an axis fixed through the center of the disk. Each disk is initially at rest. The radii of the /yb9 4af8 pa 1l)ijcd /ty.juodisks 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 radii sur3*w43+gcrr oo trlr/ch tha w *crgr3to43 or/+rrlt $r_x< r_y$. 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 radius R is puns) /g 0cyo9cplled by a horizontal force F accc o9) /p0nygsting
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 clo1 f-fn-yomiq3zx -x w(ckwise about its center with an anguzx-yn(o3wmifq1 x f--lar 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 at+h:m2rb;v4a r hlek46 - gahfnd 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 the speed k4-rb 6:h h2v eartml+ gf;4ahof the center of the cylinder when it returns to equilibrium?

  01.39: Suppose the engine amjji0 b8ho5 y 8ba- ylv0grw3ti2e -2mnd propeller of a single engine plane are turning in a clock wise direb8 0revtjow jay iym2hi5b-28- gl3m0ction 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 sharp lefthand turn.