12.43: Several forces act on a rigid body. If the resultant (net) force on the br/w,;kxcn/6n rqyl - sody is zero, ; q/s6,k nxrc -ylrnw/which one of the following statements must be true?

  97.39: A cylinder free to turnaround a fixed axis has a string wrobe jbf/d*ho80p1 y d+apped around it as shown to the right. The str+b/ fpo0hj1oye* db8ding is pulled with a force F equal to the cylinders weight. What is the acceleration of the string?

  16.16: A uniform stick is fixey1ge c 3i-53*pj rrazud to rotate about an axis through its center. The stick starts from rest 3ercgjy r 1 z5u-pi3*a 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 hasvfex0o2 wmt)i1+ a 3qc kinetic energy K when rotating with constant angular velocity. When the angular velocity is reduced to one-third, the kinetic en)+ qe3i1af 2ovc0 mwxtergy becomes

  12.33: A solid, uniform sp 0rma*)pyd(a ehere rolls without slipping 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, radius r, and rotational inezzvj-. e1j9wuur+*p crtia $0.5mr^{2}$ . 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 have1id3cp.n wt9 sy .b bboy5/ti; mass M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. The coefficients of friction for the disk iwiobn ;c1d b3tyy/. b9ps5.tand 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 epp1:lmu v-d2zach have mass M and radius R. Each object begins 1l:upmz-v2pd 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 cylinder rolls withoub o6xxj;hs*v3 t slipping on a rough inclined plane. Which one of the following choices best represents the type and direction of friction (if any) act x;s6 vhxb*3joing on the cylinder as it rolls up the incline?

  14.43: A long rod of length L is pivoted about bob*1t)p; s;nm4ayg 8fqg16n (hp,mpqbmzh3 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 rele4 1m;oh*b,6g(p3b81 npy mqpfzh q ;) atmngbsased?

  15.46: A uniform rod of mass M and length L is fixed to rotate about a frdpwhwni3uoc 2ol p+d+pc*rhi41d,(6 ictionless 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 pivoiddc1 w+h, l wo23php (6c+p 4nruio*dt. 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 isy e 0tt)fne(bj4 qzq;re qq5oz) w+4w+ fixed to rotate about a frictionless pivot located L/3 from one end. The stick is released from rest incrementally away from bein e+qz+e)z qfo rqqt40)n w;j4 5(ybewtg 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 triesze032atk hf8 t to balance vertically each of three long uniform cylinders with equal radii on the eneta z38 k0htf2d 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, hav7*(7rp ,gptwg p4+cctey oj+yr6 q q-qe 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 mas 4wrnaqvx5 0o5c by1hrp 16d1xs 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 1rxaqvyx1dp1hr o6b4n5 w50c 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 0:tr(jdf n yp+Y, have equal masses M but different radii such tha0f tn+y :prjd(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 is pulleqk +tbys*uy6ultawi : ,b n7 :mnrq098p65ilnd by a horizontaqn5ybak8ny tl ump+ti6*nrl 7i bs9,w ::uq06l 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 radius R rotates clockwise about itsu:kco ley 1-pofycz5+ :lc*,k center with an angular spee-51pkof,l cle:kccy +oy:z u*d $ω_0$ . 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 c,a2 f8j0tucju,(v yr gj9gxc *l (cw+aonnected 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 s(c+2f*c,yj9 lvjcaguu,a8 rt0( g jwxlipping. What is the speed of the center of the cylinder when it returns to equilibrium?

  01.39: Suppose the engine andr 4/+evx3 +gfgrgh3yi propeller of a single engine plane are turning in a clock wise direction with respect to the pilot. The gyroscopic action 3hrr vfg +ix3g/4+ygeof the moving parts will cause the plane to move in which direction as the pilot tries to make a sharp lefthand turn.