12.43: Several forces act on a rigid bo-; *jymv*-hvhkspk9g l )d8 iudy. If the resultant (net) force on the body is zero, which one of the follysmlpg vv-) hjhd 9k;**k8i -uowing statements must be true?

  97.39: A cylinder free to turnaroun-ch-a xcf- nx *wal(r 2ntl9/fd a fixed axis has a string wrapped around it as shown to the *l--/nfa-x(2xc hl tnrcwa9fright. 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 a/iy49dkdo+hx(*oq ) dl.lx xpxis through its center. The stick starts from rex*x hyok/idqx9d.o)(4 ldl +p st 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 empt8b,y) ,jryb ug5+znergy K when rotating with constant angular velocity. When the angular velocity is reduceduy8g,zp) t+j bb m5r,y to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls dje gj5*p mqiq b+b wmge1b;5n-e11u9 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 r8j2rz :y qkzr3, 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 idm0 s 2xd01r2 wgspsy6weal 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 formw2x02s10s d6wpsy g r 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 ha14 xdes gch1 gmf;k6q19ql/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 the f1141;/ aqsg6lceqxgm9h dkhdisk 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 pl ucfo(8 m)i+yxane. Which one of the following choices best repre um+)iy (x8cofsents the type and direction of friction (if any) acting on the cylinder as it rolls up the incline?

  14.43: A long rod of lt,6uscq.okp)x 9em -su. 2fxlength L is pivoted about its left end. It is released from an angle θabukoc)-s6 m.qpsx ftl.,2uex 9ove the horizontal. What 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 lengtfi7lemlgc8 0b g :3.xrh L is fixed 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 ir.:ibmg8e0 xcg 7fl3ls the magnitude of the tangential acceleration of its center of mass?

  16.50: A uniform stick of mass M and length L is fixed to rotate about a fr* xepa98 : kh cyorlzu.(h5ud9ictionless pivot located L/3 from one end. The stick is rele9c8uo9 r xpulh: e*k(.zyda5hased 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 lon(8c- wh 9sxvekaay)8wg uniform cylinders with equal rad(k ywhex8awa vcs89 -)ii 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, h lq j;q n/,o:rynywy)*ave 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 ro. z xf:pink.d3tate about an axis fixed through the center o.zf:p ni .xdk3f 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 ab, k4 //wvfvwta2 wt*and Y, have equal masses M but different radii such thv2,b4wfk/t w /a*t avwat $r_x< r_y$. 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 maqdu ed5o0i zoor(nk6v73 +ok5 ss M and radius R is pulled by a horizontal forcen 3z5ikqevo7 0o+k6o(dd 5r ou 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 radiu4xx mnp mrms5w714ze wd4q4y+s R rotates clockwise about its center with an d7xypwwmn44s4 xrm m4z 1+e 5qangular 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 solid2 0gaaxu0-yh0 y cq;le cylinder of mass M=2.00 kg and radius R=10.0 cm is connected about an axl g0uc-0qy eahy;02 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 of the center of the cylinder when it returns to equilibrium?

  01.39: Suppose the engine and propeller of a single engine plane are turning05ojl+4z)g 2hs+ tuul;lc qzg 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 direction as th;qtsug4 5 lc zlj)0ghzl++2oue pilot tries to make a sharp lefthand turn.