12.43: Several forces act on a rigid body. If the resultant (net) force on the ony,ka x14*v( q;twsi body is zero, which one of the following statements must be true? *qxw ;t v1,ki4ynoa(s

  97.39: A cylinder free to turnaround a fixedu q2wsss ef;;3p/n3 0iowq(dy axis has a string wrapped around it as shown to the right. The string is pulled with a force F equal to the cylinders weight. What is the ac(e3/is 0ow2 3;qnwqp ufsd;syceleration of the string?

  16.16: A uniform stick is fixed to rotatlp55 gwzq07k56rlmf ds it8u t rj.3x9e about an axis through its center. The stick starts from rest and rotates through an angle of 5uz7ttg kmflwr56d3x08r59ql .p sj i$90^{\circ}$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 ene)inbmk7qq43 1:;zvzi q qro i8rgy K when rotating with constant angular velocity. When the angular velocity is reduced to one-third iq v8o3mr: bq;741zkq z)iniq, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without swuo6l,c1dy c3 lipping 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, rd1 xpdiel 4j0-pe d)w8c 01ajgadius 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 uniforq p2j8 alid appxhs/i-r 782d2m ring each have mass M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. The co sx 2i8pdha2dp7pi/lqra2 -j8efficients 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 -n.* trqm2av/wps3m e 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 form.2ns3 /wmqat*- vpre 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 inclined plane. Which r(n xetl(hlr gtfhv:6 i/25dr4h b,q-one of the following choices best represents the type and d r/rxh4rbllnivh: g, -6te(ft qdh (52irection of friction (if any) acting on the cylinder as it rolls up the incline?

  14.43: A long rod of lep76 iw rs7ab8fngth L is pivoted about its left end. It is released from an angle θabove the horizontal. What is the magnitude of the angular acceleration of the rod about the pivot when the rod is r7 b p8r7aswi6feleased?

  15.46: A uniform rod of mass M and lenggr 1+d kqs/s82amhn o-th 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 perfsm8 +qgs hna-ro2/k d1ectly 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 w t m3/a(:-e: bgsdc) y0ytf;zpm0gwp fixed to rotate about a frictionless pivot located L/3 from one end. The stick is -bf3ypg wm;g y 0wttpedc(0:s m) /az: 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 speed of the center of mass about the pivot?

  06.24: A person tries to balance vertically each of three long uniform cylin*ul ,,v m*x(gs)fujup5) kqbxders with equal radii on the end of his fingbf)u m,jxu )*gl u(qx,vp*5kser:
• 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 massesat44 /kvsgd p*ovtwjv5 a+e 22 $m_x$<$m_y$, 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 unifozu2h tv q 7he -evpv8:;)pvw9hrm disks 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 a-tp8ehh)wup9 2 z7;qev:hv vvre $r_1 < r_2$. 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, ha; qe*o +tnc/impcj /hag 5 ))*cvoty(ive equal masses M but different radii such tha5(vt g)ht/ +ijni *);o/mpoccyc *aqe 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 (; waqw6kevkwtu 8w*8kusk98 ro 2hq0 is pulled by a horizt8q9e8s h 6wk q v*0k(ww8wu2roak ;ukontal force 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 radiustmm, u2s)ixibqxel 4+o 1.ce.+nj/bn R rotates clockwise about its ce o i. ebex+cni1x+/)t.m mq,n bju42slnter 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 cylindecfc5f3fdars/:pkb:n5/cuz/ po +g-o r of mass M=2.00 kg and radius 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 from equilibrium. When released, the cylinder rolls without slipping. What is the speekcf:/odoc /b5:gna 5 ucszfpp+fr3/-d of the center of the cylinder when it returns to equilibrium?

  01.39: Suppose the engine and prope( r6fhko9fi2. u -giqgller of a single engine plane are turning in a clock wise direction with respect to the pilot. T6fq f( g.iu- hokgir92he gyroscopic action of the moving parts will cause the plane to move in which direction as the pilot tries to make a sharp lefthand turn.