12.43: Several force4bucjq0 yc.7k-a j+3g .uvayps act on a rigid body. If the resultant (net) force on the body is zero, which a7jcjq yk+b4. .0 v p3yuua-cgone of the following statements must be true?

  97.39: A cylinder free to turnaround a fixed axis has a string wrapped axghpn3x, pa2+q/j zia +0fsx,qy 26dbround it as shown to the right. The string is pq6d,qxay 3 ,/2h+fx+ijngx 0 2zbapspulled with a force F equal to the cylinders weight. What is the acceleration of the string?

  16.16: A uniform stick is fixed to rotate about anownv+e -8fv vk23z7qf axis through its center. The szon-vq3e 2v+vff7w k 8tick starts from rest 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 fani5r de7xt8:k t-hd 6nf blade has kinetic energy K when rotating with constant angular velocity. 86 xr 7dnt5hf-:kdtieWhen the angular velocity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rxn9v) n 8wrl 7t2mbx+dolls without slipping 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 has mass m, radiuj4 s-pd n/pp-:3cmm xds 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 disk and an id xd)gfd wj1c)h9l*,ireal 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 the inr,cf*) h1ijlw 9g xdd)cline 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 qpkb;.4sl0uk x9s 2ft 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 ; fk 4s9usx.q20lpk tbdisk 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 slippiwgs1s7xlsrzg-;/ 8 n ung on a rough inclined plane. Which one of the followingn 7g 1/ 8sl;-xsrsgwzu 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 wvml+s ;hb0j9qg f;b(its left end. It is released from an angle θabove the horizontal. 9;qsh;0(flbg b+jv w mWhat 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 tow /t pmh84ln+i rotate about a frictionless pivot located L/3 from one end. The rod is w/tp8 hn i4+mlreleased 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 op9 ehekfd92o6pv z n :jy-b)t 4. 2ztyme3ry8 fixed to rotate about 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 clockwise about its pivot. When the stick is horizontal, what is the tangential sheezej9 nyzo96.8 k:my423dt vpp) tfb-o 2yr peed of the center of mass about the pivot?

  06.24: A person tries to balance vertically each of t+ p gtcrzcfhsj733,l9hree long uniform cylindersl7 rghcp3sc+,3 jt9zf with equal 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 disjxl*bwu 6:rn-u :zig:ks,X 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 diskscy4:gcz xdh0 l8u+j5 j of equal mass each are mounted to rotate about an axis fixed through the center of the disk. Each disk is initially at rest. The radii of the disks +jgyu8d0c54x zcl:h j 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 dice(,0jq.aogg(w r (ekfferent radii such that .jq0, ee(rga(kwo c(g $r_x< r_y$. 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 pnadx zl9.9,ps(o7l gby a horizontal onxpg sz ,.(d7lpa9l9force 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 rotat 1+jz;ka14jvn0pme;c5nrv n j q9jer. es clockwise about its 4; rjmz0jjc+ vjar.; v1n15p nnk9e eqcenter 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 R=10.0 (ie5 w2fdak tueq s.p0kmd+2u /+mnp5cm 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 eque up n( 25ddek5m.i0t2 w+ afpqms+/kuilibrium. 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 engine plane are turninxgcvsy b1c7t(i t2u+ 1mjk*0i g in a clock wise direction with respect to the pilot. The gyroscopiijb gtc vm(s2txyi k*07u1c1+ c action of the moving parts will cause the plane to move in which direction as the pilot tries to make a sharp lefthand turn.