12.43: Several forces act on a rigid body. If i9is dwc,15 0 nehc6mithe resultant (net) force on the body is zero, which one of the following statements must bi wccin0 ei 91dmh,5s6e true?

  97.39: A cylinder free to turnaround a fixed axis has a string wrappede v,wro, 1 3 denbxyid6.92uc,xfxu4 g around it as shown to the right. The string is pulled with a force F equal to th ,,wf2xoe.1buv6e9nc u, dxx rdy3g4i e cylinders weight. What is the acceleration of the string?

  16.16: A uniform stick is fixed to rotate about an axis through rjj,/vl 46b sabv1kd1kn.vp0 its center. The stick starts from rest and0bb4lp nj ,j1ak6 v.v/kdsv r1 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*t 7ytp7ki i6q with constant angular velocity. When the a ikq67ty7tip *ngular velocity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slipping on a floorhx +z.8b zu6d p5c:zkr 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,/gweu:)lkc0yu 3( gh*tva* ra 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 solid di rxjtzie-)/5y sk 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 the disk and ring with /x-er) z5jty ithe 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 imnusyk;7j. /wdeal uniform ring each have mass M and7/; kymnsu wj. 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 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(o 4fiemfj:84t dl ytm:*x/fj inclined plane. Which one of the following choices best represents the type and direction of friction (if any) acting on the ciotf: * m j:4mty8jx(/ ef4fldylinder as it rolls up the incline?

  14.43: A long rod of length L n7a;eb uw:+ 2naz0uynis pivoted about its left end. It is released from an angle 7n;b2n : yuan+w 0uaze θabove the horizontal. 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 frictionb3r y (n-o7l fdhw: dlgp,0olol7nl5 ;i kvn15less 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 horizontal, what is the magnitude of the tangentialo1ly7 l( lr3k-nw hpb5lo :d,i0ndl o7v5gn;f acceleration of its center of mass?

  16.50: A uniform stick of mass M and length L is x+ 94cfn .6. uaidkvemfixed to rotate about a frictionless pivot located L/3 from one end. The stick is released fr4.k6 .mxc+vdafnu 9i eom 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 bal 2zwtyue mv. kp4wx( :v58ias8wj2i;bance vertically each of three long uniform cylinders with equal radii on the end of his finger uw2ev 5pmavwbjyzi it2s4(:.8kx w8; :
• 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,ti d8-l(xs u71 bw9xhrX 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 disk:g g+ed2f4h qbwcj )*n5esy.ts of equal mass each are mounted to rotate about an axis fixed through the center of the disk. Each disk :42*fq e.te+wgj5ydcbg) snhis 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 andd2psg: 75va ru Y, have equal masses M but different radii such thags2u:d v a5r7pt $r_x< r_y$. 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 wm/56ryvw ;q; savq f4mass M and radius R is pulled by a horizontal force F am;s v y;qww/qf6 54vracting
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 my/tc 5+h(fuleps38b+n e2zq clockwise about its center with an angular speed3 cn ztshyfm+e 8(p e2uql+b/5 $ω_0$ . 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 hxmwar1vfr1z 89odo61rc hcz;z 71:g cm is connected about an axis thrw 1f hgoc;rr1 zvca8m:zxdo67119rzhough 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 pro(i 7 wwkai2lx9r s,4tjpeller 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 ia42,si w 9t(ikwj7lrxn which direction as the pilot tries to make a sharp lefthand turn.