12.43: Several forces act on a rigid body. If the resl (n,3-36w 2 wlnewn/nvwnh cyultant (net) force on the body is zero, which one of the following statements munn2v3(3l/wc e ynh6nn -w, lwwst be true?

  97.39: A cylinder free to turnaround a fixed axis has ccpv87 ,al4l8u62v,r ez6ss)wqvez ka string wrapped around it as shown to the right. The string is pulled l c 6zvw8rsqe)z6vcv l4a p u7k,s8,2ewith a force F equal to the cylinders weight. What is the acceleration of the string?

  16.16: A uniform stick is fixed to rotate aboutrll2q0- i34h+w/ 2(qn o sn;r7 cp z7txjvpoft an axis through its center. The stick starts from res;2q/wh04 q7oj3ocsl i rlpp7+r f(n-vttnz 2xt 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 bl s8:3y8zoez2 ljtgwy4 9j obq0ade has kinetic energy K when rotating with constant angular veloci9eoy8lz2z y:4 jsw0b8o qj3 gtty. When the angular velocity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slipping on a floor .r9tc t-eqks9+ o+9d q,j(od pwxvt)ialong 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, radiusfr(b nf k8q6- :xr3yrr 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*bbvnrxo50pb l ;r4-nm solid disk and an ideal uniform ring each have mass M and radius R. Each object begins pu;n0p lnr4br*ov- bxb5 rely 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 M andjf-w;b e ,(b a7kgn2yt radius R. Each object begins purely rolling without slipping down a rough inc-;t7fg2bkb,a (enwj ylined 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 ic2dd(w.u/-*- em2h t(fc (fb jpeb ycfnclined plane. Which one of the following choiccb-b/*p. fm- ewf(d((2thf djuy ce2ces 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 is releasedpl ve/hyy2sk7 .lu 7k( from an av7yl/. p(ks 72yeuhl kngle 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 ld6hyd:tc s 9pd/u(p ,/j-xrs is fixed to rotate about a frictionless pivot located L/3 from one end. The rod is rel9dud rt(jd:/s,h/c-xs6 yl pp eased 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 tangential acceleration of its center of mass?

  16.50: A uniform stick of mass M and length L is fixed to rotjp:e88q u kfz1ate about a frictionless pivot located L/3 from one end. The stick is released from rest incrementally away fpk1e:qf88 uzj rom 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 cb3zp-0x 3 bnuuylinders with equal radii on-0nbu33xuzb p 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 masse4:ug n(o.eacd.cne0 bs $m_x$<$m_y$, 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 equal mass each j/u ha(cxi8v)nyuk 7tc/r7 ;iare mounted to rotate about an axis fixed throu8)ukc;urtxj (h y7nia/ivc7 /gh 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 diotdsw ,k /w 8jdpht/7s ::ui-3avwub2ya:j7d sks, X and Y, have equal masses M but different radii such 73y-vob7/d:t/tw2 dia, w p:uusksa8wj:jd hthat $r_x< r_y$. 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 ia fop/2odrk c-zw35;6har x7 a mass M and radius R is pulled by a horizontal force F acting o5o rrkfi2c3ph67 / axwdz-;a
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 clockwise ab e- 0wc3l/fjfdout its cef elw0-fj3/ cdnter with an angular 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 q 3(i; yb.i 0sx+rpemhR=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 of the center o( +0se xrpqbi h;iy.3mf the cylinder when it returns to equilibrium?

  01.39: Suppose the engine and propeller of a single en 2f2fmuc1ujmu1k 19ccgine 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 direction as the pilot tries to make a sharp l9cm1c 22j1ufu1f cumkefthand turn.