12.43: Several forces act on a rigid body. If the resultant (net) force od1a k1kh o5gv(n the body is zero, which one of(kvk5dh1ag1 o the following statements must be true?

  97.39: A cylinder free to turnaround a fixed axis has a seml1)zm a-sb s9fwm a 3ns54e5tring wrapped around it as shown to the right. The string is pulled with a force F equal to the cylinders weight. What5-aml31e 95)nf s 4mew bzmsas is the acceleration of the string?

  16.16: A uniform stick is fixed to rotate about an axis through its cente yt(r:dmil p,6kc 3-qk9hg9oc r. The stick sta9q-k :ychdtm k3pli (g9,6roc rts 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 fanesjf(bt 8m-7 o blade has kinetic energy K when rotating with constant angular velocity. When the angular vem ef78obj(t -slocity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slipping on o)ycnad jj kpsg;3 :gx-1q* (-nzibg; 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 rotationa prac((w,(ys k;zxv 8ql 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 zx:wuc +9 h.hpsolid disk and an ideal uniform ring each have mass M and radius R. Each object begins purely roll:z x.+huwp ch9ing 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 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 dizu:x.lo,t.yln y*xrj 9d d 2z;sk and an ideal uniform ring each have mass M and radius R. Each object begins purely rollin,t; : jrd*lz yxul d92y.z.xong 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 without slipping on a rough inclin8wqzsvfe0 lgwyc dg 8nv(j k*78wur,l/-r4v+ed plane. Which one of the following choices best represents the type and direction of friction (if any) acting on the cylinder as it rolls up the incl4wvys,07rgv jz*88 kdv+ w-/ 8lqne( wcflugr ine?

  14.43: A long rod of length L is pivoted about its left end. It is relp1 jhd+i1 .zs2ke2wfseased from an angle θabove the horizontal. What is the maghj12f+k 21zws s.epidnitude 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 fsl 7o.9 ,svggoixed 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 7 lovs,gogs .9rotating 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 i90ge.ji4e : q r;zy 8v62g ljb6bxljtjs fixed to rotate about a frictionless pivot located L/3 from one end. The stick i x je4qbzt9g06ij;lly6e:8jv.bjgr 2s 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 cy ,3,7 fiqyync umj4tv: f(x((yc,ynl, v5jflm linders with equal radii on the endj7( lfyl,t(y f53yx ucnic:nj(yv,v q4 m,,fm 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,k17q+.mjb tyv 4 yps:v o*xtdf+bpx 66X 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 rotatl),rya2av2 b be about an axis f ba)ba, 2ly2rvixed through the center of the disk. 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 masses M but diffp 00zatudsbn(u9,h1 perent radii such that s9(pz1udbt ah 0upn0,$r_x< r_y$. 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 wis*8 +tdfw2j-4rz nwrkqe+s0 q th a mass M and radius R is pulled by a horizontal force F a *zrtnqwe-82s0++jfd w4rkqscting
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 rotwr36z 3hj6ey vates clockwise about its center with an w h6z e3yvj63rangular 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 cm i2l 0 bjhpz5g)ps connected about an axis through the center of the c52ljp p0 g)zbhylinder 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 of the center of the cylinder when it returns to equilibrium?

  01.39: Suppose the engine and pa9v-uapo bbt.;pm 2 m+ropeller of a single engine plane are turning in a clocua.+t 9mm;bv2pp-b aok 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.