12.43: Several forces act on a rigid dfh*gx 2l hhmk1.1cf :body. If the resultant (net) force on the body is zero, which one of the following statements must be true?c hh1k2f fd*:1x.lgmh

  97.39: A cylinder freyzu,l u ,x1z.me to turnaround a fixed axis has a string wrapped around it as shown to the righyzl,ux m1,u.z t. The string is pulled 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 an axis through its croccx. 6 n.sh;enter. The osc.rc6. ;nxhstick 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 fan blade has kinetic enenk2 j2 p,iplx++(mr dkrgy K when rotating with constant angular velocity. When the angular velomi k+(2d2l+,jx kp rpncity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slipping on a floor along the08xob+/f 5ru k grmri1 $+x-axis$ (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, raatz m2zi83(ossvqd5 i(t+) 0ehlgx p2 dius 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 ideal uniform m6bf, hcu6nb 1ring each have mass M and radius R. Eacfh6b c,nb6um1h 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 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 solin *r0lwm)o: x g.qy-gvd disk and an ideal uniform ring each have mass M and radius R. Each object o n*r:vlg)q.y x-0mgwbegins 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 cylinxaeq z8b:i3 f3yv -9rader rolls without slipping on a rough inclined plane. Which one of the following choices best represents the type and dire8a 93iefyzrqa-x3: b vction 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. Iye5aq,r ) r5uw yeilru3.84vzt is released from an angle θabove the horizontal. What is the magnitude of the angular accelerationyr v4u5aeli.)rq y,zwur 35e 8 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 dnmxfpb( 2st:p; i1.wfrictionless 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 magn bpf2s m;dwx:.p1n it(itude of the tangential acceleration of its center of mass?

  16.50: A uniform stick n7td mb*dxxc.6z-+sz of mass M and length L is fixed to rotate about a frictionless pivot located L/3 from one end. The stick is released from rest incrementally away from being perfectly verti.sz* cdx6bt-nxzdm +7 cal, 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 each5imtovkwd7kp4;ww 6ezs 0 k,y6 a;c7 jotte-) of three long uniform cylinders with equtv7kwtp4koecsi )m5 zkedot70a yw6;6 ,- ;wjal 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 andY, have massekstr cx*r wv z0kg,m2i94z3p8 s $m_x$<$m_y$, 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 mabz 9bhi5;ld 1n4 .bpea 4q2frjss each are mounted to rotate about an b;5nb. 44i2dza jf9eblq p hr1axis fixed 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 masnp-iqh0 890 4uluecqjses M but different radii such thc4jl 0h8 up-ui9enqq0at $r_x< r_y$. 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 pulled1i5kkw q; d0(dxoqt :ws x8z uy6;lzn4 by a horizontal fzl wy s;z;6 ux1(ikd4wk0 qnx q58:odtorce 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 rotates clockw*g9 )we iu br1a2x-pivise about its b2 )ip9x*1ivgruewa -center 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 re/x:cnjafss7 y5;nss06 7imcadius R=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 fromy7s7:i6a /njfx s;cssc 0mn5e 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 aga:j4f; 88 huqruf v,propeller 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 in which direction as the pilot tries 4f8u rjh:qa8 ,v; fguato make a sharp lefthand turn.