12.43: Several forces act on a rigid body. If the resultant (net) for7,nadu c3r -axce on the body is zero, which one of the following statements musrnad -7c,x3u at be true?

  97.39: A cylinder free to turnaround a fixjx*mxos a, 3z;8wsjt*ed 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 t,at *j z*83ssxxj m;owhe string?

  16.16: A uniform stick is fixed to rotate 5z70 q vn7vi*xiywue0about an axis through its center. The stick starts from rest and rotates through an angle u*q vye0x0iw7 7 z5vinof $90^{\circ}$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 ki*7/eb/b w7hn nn8e;z*obc unlnetic energy K when rotating with constant angular velocity. When the angular velocity is reduced to one-third, the kibnu;h 7/e8b7 n e*lnc/*nozbwnetic energy becomes

  12.33: A solid, uniform sphere rolls without slipping on a floor alo pa):dycmn w5i jo:r8/ng 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 inert ce0q q-.(tm8foiqm1h ia $0.5mr^{2}$ . 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 idgii p7gi6op:, hoa/a: eal uniform ring each have mass M and radius R. Each object begins purely rolling without slipping down a rough inclii /7pii o:h:, oggapa6ned 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 62clwwk sd8mj 4 g*iu/uniform ring each have mass M and radius R. Each okidwjs2 *l/m4uw6g c8 bject 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 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 roueaay.1s/rqda9 6vg2r/ qb 9imgh inclined plane. Which one of the follbaadrgm99q q /ay.6sr/21ie vowing choices best represents 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 L is pivoted about its left end. It i 4,;vgapw7d f/ 1ubcqvs 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 released? 4b/1qd fucvvgwa7,p ;

  15.46: A uniform rod of mass M and len+j,ho;hwkltzob :q5)9 pn , pnchx 0b8gth L is fixed to rotate about a frictionless pivot located L/3 from one end. The rod is released from rest incrementally away from being perfectly vertical, resulting in the r+;ox,nbq)nb: pzjlhwcht9k 8,op05hod 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 *x2f r j2vfb)mabout a frictionless pivot located L/3 from rf*fj2 vbx2)mone 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 mass about the pivot?

  06.24: A person tries to balance vertically each of three long unifor8d gtv;rjg1*a)ccasa4a ; y7(pw/w abm cylinders with equal radii on the end of his fay*wcaa /a c8s74atb gpgd);; (w r1jvinger:
• 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 masswb4vd/:gqkri h 62hm 3es $m_x$<$m_y$, 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 uni -,e.tsd+pwo ix ap8.zform disks of equal mass each are mounted to rotate about an axis fixed throu+osd 8t ,-ze iwpx.p.agh the center of the disk. 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 *rp+-*o6idw5ge /pvacvcx-l and Y, have equal masses M but different radii such thata-l+rci-w* p*gd6pxe v 5v/ co $r_x< r_y$. 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 pulled guisr, otuq30//r y+ pby a horizontalr//,0+ gtusquyp io3r force 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 anu f ec-,jn(vx/d radius R rotates clockwise about its center with an angular spen,f/e -xuj vc(ed $ω_0$ . 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 v9. du9*fcllz 8x2 *)vwhp7fuhoo4nxM=2.00 kg and radius R=10.0 cm is connected about an axis through the center of th.u*x7 phncf vd8* o9z9u2ollx) wf4vhe 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 propeller of a single eiy nni ejwpxz(w 0d7r8 )dz);1ngine 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 directi)0;dp8zx jn)1 id(eziwnwy7ron as the pilot tries to make a sharp lefthand turn.