12.43: Several forces a ir hl4+e4a(0q.4jt*(a kreqk c(ue nuct on a rigid body. If the resultant (net) force on the body is zero, which one of tuurkki(4a4t +.(hcn4eq( el* qe 0jarhe following statements must be true?

  97.39: A cylinder freqjtm vrb1r06d1(y tbt- 1l/pqe to turnaround a fixed axis has a string wrapped around it as shown to the rl/bq61r01 tvqtdyt(bjr1 p-might. 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 c+l h0:obzko 7benter. The stick starts from rest and rotatesozbl7 k+ obh0: 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 energy K when rotating with constant 10+f4sxno 4b:nr 9 vl5/mo zd enm;xhqangular velocity. When the angular velocity is reduced to one lqe/rd5+v:nm 4mxnz ohofsn4x 9b0 ;1-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slipping on a flo)jmam4*wp2 mcor 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, z ,o6m.r xifw7radius 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 ring each have mass 6/b19soen qvwM and radius R. Each object begins purely rolling without slipping down a rough inclined plane. /1wqoev6b9n s 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 an*khg2g iesw+ 5d radius R. Each object begins purely rolling without slipping down a rough inclined plane. The coefficients of friction for the disk and ring w2s+kgh5 eig*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 inclipjwq7bqg109 2 wi d gfsq.)h7fned plane. Which one of the following choices best represents the type and direction of fri 7f d90bg1.jq w2)pqs7 fwiqhgction (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 relea-/sw:gxb yohh cn/s.l) qk77 65rmclcsed from an angle θabove the horizontal. Wsqrh )k x mc o/ l7g6w.-:y/lh5sccb7nhat 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 to rotat4 ec 88nw*6 d e+c:khndtjau9ge 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 is the magnitude of the tangenti 8+cwu nte4ed:kn69 a*dg chj8al acceleration of its center of mass?

  16.50: A uniform stick of mass M and length L is fixed to rots 9 -wlnfi 1c+j:lev5bate about a frictionless pivot fsne will+: 5j-vc1 9blocated 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 speed of the center of mass about the pivot?

  06.24: A person tries to balance vertically eachrbvdfw -d-o8rrbfazq 1e7/p n85 np+) of three long uniform cylinders with equal radii on the end of his finge8b/pd ovbnrn-qw )f-df1 z785+ rpearr:
• 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 die( y:jn6roj z-a3h+x9xdfwl5o0n -p g k q;6hrsks,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 disks of equal mass each are mounted to rotat8 zshnbn.3m;y1m fp(le about an axis fixed through the center of the disk. Each disk is initially at rest. The radi1 (3sf8mny;mh p n.lzbi 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 bu/kebj:( ox5qg(w czy 4t different radii such that :4(/c(g 5yeozkqjbwx $r_x< r_y$. 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 igi1068d iud qns pulled by a horizontal for i06d1igudn8q ce 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 clockwise au-*+k 2ca 8i/goo k-1 n shecoswjbp)8bout its center with an angular speed ase-bchwk i-2oncgj* sp)818 uo /ok+ $ω_0$ . 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 cm is cdsx z. y+;: lcu8v: i:*dulvhwonnected 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 vhx;w*l vy i.d+lud:cs:8zu: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 engine and propeller of2kg / pttook5- 65slox 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 pltkxs tk25o op-lo/6g 5ane to move in which direction as the pilot tries to make a sharp lefthand turn.