12.43: Several forces act on a rigid body. If the resultant (net)x: .a/pm,enzr1vy*u f force on the body is zero, which one ofmz:vaf e/ u, *x.p1nry the following statements must be true?

  97.39: A cylinder free to turnaround a fixed axis has a string wrappo810p;l9 alzimu r 1yqed around it as shown to the right. The string is pulled with a force F equal to the cylinders weight. What is the acceleratiop qmay1zl;l98ro 0i1un of the string?

  16.16: A uniform stick is fixed to 9ty6/f +ukqm qb)qss /,zfr (srotate about an axis through its center. The stick starts from rest and rotates through qs, b +fqmsutf/(ksr9q6) y/zan 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 rotati*u);bc- mhf;6 ps1)j gbgn watng with constant angular velocity. When the angular velocity is reduced to one-third, the k;bpm6hau 1;c )j*)sfg bwg -tninetic energy becomes

  12.33: A solid, uniform sddfj1l 4 (4aahphere 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 ha yv8m -xwhy9iu::w 69wr3g kxms mass m, radius 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 5g6(n omzjms:*-lpdxh,y e6f and an ideal uniform ring each have mass M and radius R. Each object begins purely rolling without slipping down a rough inclined planedexmns: o*6l -,6gyj5(mfhzp . 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 each have mass M andao5 hq a24-fsv radius R. Each object begins purely rolling without slipping down a rouq-v a2h 5asf4ogh 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 inclineddblf jc;k)( m9o4 dg(r plane. Which one of the following choices best re(mjf(lk9bd cg) ;d4orpresents 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 its left eu 8( pn : .-0chpp*hjray8vdognd. It is released from an angle θabove the horizontal. What is th0oc :.*nvu jap8p rp- h(8gydhe 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 length L is fixed to rot-c)c)pt/ajlx0 ko y)n ate 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 of the tangential acceleration of its c)ajlkx/-p y)nct o0 c)enter of mass?

  16.50: A uniform stick of mass M and length L is fi*a d,:id ydn9qxed to rotate about a frictionless pivot d,iqd*9na dy: 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 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 cylinder3d*h tf6: ebkes with equal radii on tht*k36f e dbhe:e 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, have mas fhr() vgdww-n5k3v3 x;q.r slses $m_x$<$m_y$, 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 uniformmyio+:8qh2dtg f 1f+l disks of equal mass each are mounted to rotate about an axis fixed through the center of the disk. Each disk is initially at rem+ygo8qif dt2h : +1lfst. 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 M7fhlpculvyenqm0 0;s ui mmd(y3// i6l n6q54 but different radii such thatq0u(sl36ymlvi7qy 5 6n f4ip m/n; 0elm/uh dc $r_x< r_y$. 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 pulled by a hor15)ahjld+bw 1j4tztbu / vq 7xizontal force F a+t75u w b)/hztldv 11jj4qbxa cting
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 aboutefjfxt55+6 1 1tpmbc(s- ckkr its center with an angular s(+rsjfp ce kf6 m-b1k5t5c1 txpeed $ω_0$ . 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 hf8sop (uigz ,atjq; t/5x3u)onnecthigo/ ;8 us ,3jtq5xzp)ftau(ed 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 returns to equilibrium?

  01.39: Suppose the engine and propeller of a single engine plane are turninoe-7b m1s hwy;g 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 the pilot tries to make a sharp lefthand turn.yw be -ho;m1s7