12.43: Several forces act :7g3b vepa1q5bxc;c**o h bfxmok17f on a rigid body. If the resultant (net) force on the body is zero, which one of the following statements must be tru: xboxoq7cf;c1b hpe*531m ag* k 7vbfe?

  97.39: A cylinder free to turnaround a fixed axis has a string wrapped arofvd1q1hzenw w-8 6)p hund it as shown to the right. The string is pulled with a force F equal to the cylinders weight. Wha)wp81eqdh -n 6vh f1zwt is the acceleration of the string?

  16.16: A uniform stick is fixed to rotate about an r, jf v.l55.s 6gr 0vxcm)iplnaxis through its center. The stick starts from rest and rotates througjgr xs5l,r c 5mn.06fpiv)v.lh 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 with cdnby5 bgxq j,o9pa:a l e8,y9/hh(u 9nonstant angular velocity. When the angular velocity is reduced to one-third, the kinetic energbl9opdj/(xan :q 9h5a, ,y8bheun9gyy becomes

  12.33: A solid, uniform sphere rolls without slipping on a floor alo tkexiins+ 76lp(2)hb2;fgrd 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 h k+xas zqwb)(7as 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 solj oyqvam8 sr)cg-lug+k0-d08 id disk and an ideal uniform ring each have mass M and radius R. Each object begins purely rol+88 kravc)0uydqg--gj0mol s ling 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 uniforbaw0*r2ty .z55oe z kym 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 witz5y.5akoyr *bzw2e t0h 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 o)ue-u ;bgox /rhc - h6hke+i)-np0pdbn a rough inclined 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 inc u u /6rb -i0+h-b exo;nhh)e)cgp-pdkline?

  14.43: A long rod of lex0g8m /6rj3kze8)c4pddps/ eung;3m xba j /ength L is pivoted about its left end. It is released from an angle θabove the horizontal. What is the magnitude of the angular acceleration og3ak/ /m;x3zeg4scnpddjpr 0/ujb8 8e )e x6mf the rod about the pivot when the rod is released?

  15.46: A uniform rod of mass M as4q pw8t,:vc+yan u:p nd length 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 rod rotating clockwise about the pivot. When the rod is horizontal, what isau,yp +w:n8q4scp: tv 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 aboxw*s:4udai,dc r2a v4: bx2 rrut a frictionless pivot located L/3 from one end. The stick is released from rest incrementally away from being perfectly vertical, resulting in the stick rotating sr :rux22wx*i c ad :vdr,ba44clockwise 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 vezei dr znv:lh266iep(r -uz3n5 ;mbz3 rtically each of three long uniform cylinders with equalm z:(bi-zrne; 66v zniu53z2ed lphr3 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 )k)h dqau kjskfa4 hjyiw 8/( 7.q8z,dandY, 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 equal mass each are haaf,pvn/zk k09+trmo 4kx.e y ,q-p4mounted to rotate about an axis fi40vx k- m ,e rhyzqn,a.9tappkkf4/+oxed through 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 and Y, have equal masses M but different radim/ xc0 uxkrk2j u qvzfk v8t.0e4p5)f3i such thavupfq) 5f84txr /ukxjkkemz2 c00 v 3.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 M and radius R is pulled by a hortoy ) mq)f(iq )-2qlra p 2dziz6xj8d6izontal f6x taiyz-22 q jdrzqiqpm)d)) o( l6f8orce 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 l,fj- 6 7z/,mowgcqqc of mass M and radius R rotates clockwise about its cenj/mg,, ccowzq-6l qf7ter 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 u.nd5b mp e(k-and radius R=10.0 cm is connected about an axis througn -mbe kp.u5d(h 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 erzm 8 7 n+eg7jpi+)t4s*tilsbngine and propeller of a single engine plane are turning in a clock wise direction with respect to the pilot. The gyroscopic act+t)7tsb p+n j izl4*gisme87rion of the moving parts will cause the plane to move in which direction as the pilot tries to make a sharp lefthand turn.