12.43: Several forces act 3q i+h f t7ajs( *,nf(sicn,q6io 7vwlon a rigid body. If the resultant (net) force on the body is zero, whichi,c(o6 f77ws na3lv (i,jqqf*tish +n one of the following statements must be true?

  97.39: A cylinder free to turnaround a fixed axis has a strov5fm14 n)esk90cc :v xhbf,king wrapped around it as shown to the right. The string is pulled with a force F emf)5c,409c fbk 1nh:vksoxv equal to the cylinders weight. What is the acceleration of the string?

  16.16: A uniform stick is fixed to rotate about an axisvp.,phkm ks 1;e(pc 5j through its center. The stick starts (5 1 k;epvjhp,p cm.ksfrom 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 when rotating with osqdf* 5sa z-oxjmm* ttze4-3ou/9w1constant angular velocity. Wh-1m*ej3 st/9 zwzoto -a4s5*qom u dfxen the angular velocity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere-s1hx0 *-:+usjvm,u ja:prwlgr n6 sx 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, ral)q06 d ah:ogl0xv q3vdius 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 uniform solid disk and an ideal uniform ring each have mass M a *on)oo,(jj( x9cp73u fjz jpfnd radius R. Each object begins purely rolling witjj 3ffopxn cj7*jz( u)op ,(o9hout 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 disk and an ideal uniform ring easd0o phw*oa8( ( jk:io7 5yswech have mass M and radius R. Each object begioykw8d 75 wsj(*e( a :0ioosphns 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 withot3-zv hrxmoqy d (+jb 39j/3urd/ hsn8ut slipping on a rough inclined plane. Which one ofz/9dbutx sj3qmdr3hh(j v-8/ o nyr3+ the following choices best represents the type and direction of friction (if any) acting on the cylinder as it rolls up the incline?

  14.43: A long rod of length L is pivoted about jc 4-yfx9 po:bits 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 ro9 :4-xyc fpojbd is released?

  15.46: A uniform rodh; eplz0 i*( *bz topd/ojwky7qi); x2,.aeiq of mass M and length 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 wx q*zl;i/)o pboe7hd(ez., q0k t;pa ij2iy*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 is fixed to rotatvg t d*gkr(f9.t4/qmlgx+5 pqe about a frictionless pivot locv.mdggrk 9(+l* pt xgq/q tf45ated L/3 from one end. The stick is 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 vert );1nu/wqh5uum7v, kuzotl n 7r8c-xu ically each of three long uniform cylinders with equal radii on the ec u1nuow;/5lvru8 nztm -u7x7uqk) ,h nd 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, hczt y6hm4e. 4kave 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 eq5xn o5(clwk)+u8xy on ual mass each are mounted to rotate about an axis fixed throyx5o noku cn(8lw)+x5ugh 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 spv8f 5ac w r(57c8x1b*lzesc Y, have equal masses M but different radii such 8ebcclpv5cwa57 sf1 zs *r x(8that $r_x< r_y$. 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 radiu5 i2dcob/(pwq s R is pulled by a horizonoqc2b5i/p d( wtal 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 ofvn omxbs.5y5cg.xg32 mass M and radius R rotates clockwise about its center with an angul v 5 3.n25gbomy.cxsgxar 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 solidafa; n, dw0(qg cylinder of mass M=2.00 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 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 ; wad(qa0f ,ngreturns to equilibrium?

  01.39: Suppose the engine and propelle7u/ic , rwjyt0r of a single engine plane are turning in a clock wise direction with respect to the pilot. The gyroscopic action of the moving parts wiu/ cw,j 7iy0rtll cause the plane to move in which direction as the pilot tries to make a sharp lefthand turn.