12.43: Several forces act on a rigid body. If the resultant (net) force o )u( ,zgsyam5bqg-nh8 a0z2 / nwfose 1.pld;dn the body is zero, which one of the following statements must be tzd8f0apah zd,l5o/ n1yse2mb g )(qn.- wgs;urue?

  97.39: A cylinder free to turnaround a fixed axis has a striz( :i* d2pebk;y*wxpsng wrapped around it as shown to the right. The string is pulled with a force F equal to the cylinders weight. What is the acceleration ofzes2*i bd* ( w;ypkxp: the string?

  16.16: A uniform stick is fixed to rotate about an axis 0jfpdx h5 uy3qp:e1+sthrough its center. The hyqp0jp:f5 u x +d1e3sstick 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 w h3t2tvc c1o:jr)(hmenergy K when rotating with constant angular velocity. When the angular velocity is reduced to one-third, the kinetic energy becomeh3vhcw1m:r c(tj) t2o s

  12.33: A solid, uniform sphere rolls without slipping ow2.l-bo r+px szhkd7*n 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, radius r, and rotational ine sb tz*9f8gpuaxnx1 y)z -w )5uets;;artia $0.5mr^{2}$ . 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 /g *u+ ntz6cguhave 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 inclint/u zgcn*ug +6e 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 anzi;,;xfg eppy.yq /vdd y32h*d an ideal uniform ring each have mass M and radius R. Each object begins purely rolling without slipping down a rough inclined plane.d ;hiqefz/xypp;* 2v 3y y,gd. 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 cylinder rolls without slipping on a rough inclined pla; ;oj/b xe4up.z pvr*v0nkw; gne. Which one of the following choices best represents the type and directionugvp z/.jv0;xr ;k*4; pwboe n of friction (if any) acting on the cylinder as it rolls up the incline?

  14.43: A long rod of length L5 6+- rz9uxu :3e musm*lfjzo)in hji( is pivoted about its left end. It is released from an angle θabove the horizontal. What is the magnitude of the angular ziunr um9 u *6lh :jj5xs)fzmoi+(e-3acceleration of the rod about the pivot when the rod is released?

  15.46: A uniform rod of mass M and length L is fixedofcsn/ph:1 g9 ntr 0 tg gm2 tgozc1l*,p*2)sp to rotate 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 op2r 0pfo1gz/,gl tossmh2 c*)cp gn:t1*n9gtf the tangential acceleration of its center of mass?

  16.50: A uniform stick of mass M and length L is fixed to fj, jzsqgir)ts2 ghe/(2f5c5 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 ise22f zr(gghci5j5/sq )t f,jts 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 cf5 +ap ss9s9*;devbfd ylinders with equal radii on the end es*;fsf5 9+ a 9dbvdpsof 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 d ,q :uz5usm5rcisks,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 aretvk;-efl 3jb6 mounted to rotate about an axis fixed through the center of the ;fjl 6k3e v-btdisk. 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 mass)b zsewzm7e d9y fd52*es M but different radii such twbee5z7 yzms d* df)92hat $r_x< r_y$. 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 -hgpx6yiz4o); zz:k jetxd 5.8yy2qw R is pulled by a horizoe d5yh2x:k4 oz 6;8ty-ig p.zzwx) yqjntal 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 ok* q gd)jdc6p;f mass M and radius R rotates clockwise about its center with an ad d;)6gqcj *pkngular 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=2.0b7h1nnk( )+kznq ,5vvgvll5 t0 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 backqb1g5(vvn7n5z v )k ,kth+ nll, stretching 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 propel*ica fz;qk)phj7t.r1tnu.+v ler of a single engine plane are turning in a .t;ci ) ua nvtjr+qz7*hk.1fpclock 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 to make a sharp lefthand turn.