12.43: Several forces act on a rigid body. If the resultant (net) for4rx1t/t ztzkqx:4 f1yce on the body is ft1t4r y t x/14qzz:kxzero, which one of the following statements must be true?

  97.39: A cylinder free to turnaround a fixed axis has a string wrapped artmtp h0 dd:;-bound it as shown to the right. The string is pulled witdtht 0 d-bmp;:h a force F equal to the cylinders weight. What is the acceleration of the string?

  16.16: A uniform stick is fixedwnho /y7me 71j2w e uc:wiie)7 to rotate about an axis through its center. The stick starts from rest w 2c7o 7n wi7 wjey/)hu:ee1im 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 blade64r 4n*jpvf)p unc tw9 has kinetic energy K when rotating with constant angular velocity. When the angular velocity is reduced to one-third, the kintj 4pp6ucv9* w n)f4nretic energy becomes

  12.33: A solid, uniform sphere rolls without slipping7aoa*a w-t;d g 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 haw6cl,6fgcm 2wyi5c+ ks mass 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 uniform sdkhzgb,vl6j( my7v*- olid 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 friction for them(kvd7,g zlvbj- y*h6 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 hav82xtkl6 c r6;ws6bwn ye 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 ib6wwr8n ;t 6l2 xksc6yncline 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. W y bkncin. anmth1,kc4c301s )hich one of the following choices best represents the type and direction of friction (if any) acting on the cylinder as it rolls up the ik . c4, m3atnnb)0ih1scy k1cnncline?

  14.43: A long rod of length L is pivoted about its leftkx/qjb3ezl hv1u bycni*)2;. end. It is released from an angle θabove the horizontal. What is the magnitude of the angular acceleration of the rod about the pivot whenqhb neb 2/i3 x1 ckj.*uzvl;)y the rod is released?

  15.46: A uniform rod of mass M and length L is fixed to rotate about a moya39cs,4ka tk :r6hfrictionless 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 pivot. When the rod is horizon crk,k4y aht3msoa69:tal, 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 mh5k jfm cw )h;1ka;/c(drby( to rotate about a frictionless pivot located L/3 from one end. The stick is released from rest incrementacj( k wh;f(dk mhyc;br 5m1/)ally 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 verticallye;kx 1.; my l+xvq(wc ,7bedsd each of three long uniform cylinders with ,(dxyle .+bqdc;1;7 wvx ksm eequal 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 masx;veeu /u;jli. y)e130bn hpises $m_x$<$m_y$, 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 dj9 r* 237flm *rviorbu3u ekb4isks of equal mass each are mounted to rotate about an axis fixed through the center of the disk. Each disk is initially at 2urjkvr 3ofl37 9* bm*ubrie4 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 differej azo +zd;d 7guo+.b0ent radii such thaoudzj 7;d.0 +gbzaeo+t $r_x< r_y$. 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 bv9dnw4ll f/ g91rgbtb,nn9*M and radius R is pulled by a horizontal fodt4b9b 1lnb lgf *9 rn9,gw/nvrce F 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 disk of mass M and radius R rotuj,lwjr tdvqa1o0,g- *e6s5 lates clockwise about its center with an angular s1*gewvt,qlju l6sr, 0-5 djo apeed $ω_0$ . 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 mas0m(yp/k btzt e i-+mhe(a9l r-s M=2.00 kg and radius R=10.0 cm is connected about an axis through the9k p-y+0h-rb(mtmiz t e/( lae 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 e/.dvgf z3uixc *aqb4 ,ngine and propeller of a single engine plane are turning in a clock wise direction with respect to the pilot. The gyroscopic action of the moving pzbf. /g4i*cua3d ,vqxarts will cause the plane to move in which direction as the pilot tries to make a sharp lefthand turn.