12.43: Several forces +7 vzq9ngr (g+ lan3szact on a rigid body. If the resultant (net) force on the body is zero, which one of the following sts+v 9alg+ z(73q rgnznatements must be true?

  97.39: A cylinder free to turnaround a fixedcyk(s,llf s h3kd q75ts6z2(v axis has a string wrapped around it as shown to the right. The dyk36(lq 2 (h5ss v,lkt7zf csstring 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 ai 8 kdes4.mj(kxis through its center. The s( i.se 4dk8kmjtick 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 energy K fm b34ixob zu58xfx7.when rotating with constant angular velocity. When the angular velocity is reduced to one-third, the kineticfb f85ubx7ixmz 34.xo energy becomes

  12.33: A solid, uniform sphere rolls without slipping on a floor along thtc:x3( jjevnqb6 lq442 h(kj je $+x-axis$ (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 masg(0 x+d9tuijfxd8-vb4 ikjb.rw .ns. s 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 unif ru6cls5i)a1y orm solid disk and 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 for cu5 sia)1r6 ylthe 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 riz 4hv 9 4s:th+z/ehlbing 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 incline are z li+e/v sb:4 h49zhht$μ_disk> μ_ring$.
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 zh6vxb ugs5thj+k 2..a6o-ffslipping on a rough inclined plane. Which one of the following choices best represents the type and direction of friction (if any) acting on the cylinder xo- jsh+v26.zgfhf65 bua.kt as it rolls up the incline?

  14.43: A long rod of length L is pivoted about its le4 3pn xrt/k(0du/4a byehd3b yft end. It is released from an angle θabove the horizontal. What is the magnitude of the angular accele4 4n3y /k/0tdrbeahupb(xdy3 ration of the rod about the pivot when the rod is released?

  15.46: A uniform rod of mass M and lel; t)st+hzzd q6n s+3fngth L is fixed to rotate about a frictionless pivot located L/3 from one end. The rod is released flzqtsz3tf sdn+h +6 ;)rom 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 g2+bff (j+.j+sygy+o4dm0o lj )tqlhmass M and length L is fixed to rotate about a frictionless pivot located L/3 from one end. The stick is released from res+gtf(++0 osb y4y) +mjl2ogqjfhld j. t 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 vertic7 ;xahsh e*y.hally each of three long uniform cylinders with equal rx y;*.7h sehahadii 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, s lsj6z.(rtc: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 rotate a,wk ,m/y/a+yz;s. v -5l3 cvhj dasifpbout an axis fixed through the center of the disk. Each disk is initialadwz,pfi-y/+ckh .v; / 5 ylmsv3 ,jasly 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 differentpv+acix8y 0 6ro )oh5k radii such thai8r0yoa h6+ okpc)xv 5t $r_x< r_y$. 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 m7) da-vk9kybw, i p6rb0z lg*fass M and radius R is pulled by a horizontal force kgak,v if-y)70z9p6rl w *dbb 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 ctgonkf i )s:5:lockwise about its center with an an i5os)ntk:fg:gular 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 cigiexz-9v g ;;m 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 speed ofg9eii-;zxv; g the center of the cylinder when it returns to equilibrium?

  01.39: Suppose the engine and propeller of a single engine plane are h wo9*cm17tqzturning 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 q9who* m1c7tz direction as the pilot tries to make a sharp lefthand turn.