12.43: Several forces act on a rigid body. If the resultg: vkvyzm2 )+dant (net) force on the body is zero, which one of the followi: +2kz)mdvyvg ng statements must be true?

  97.39: A cylinder free to turnaround a fixed axis has a string wrapped around isbv1 +s( rkm09b/exy 7brdup/ -umjgkq4 0-pkt as shown to the rvx0gj0uk- b s r1//sdbe9bp q(umr 4pymk7+-kight. 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 is5y85 b0ahimw c fixed to rotate about an axis through its center. The stick starts from rest and rotates 0hac miw 5y58bthrough 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 wghfbvzt e*n 9/u0 k56.xk el.rotating with constant angular velocity. When the angular velocity is reduced to one-third, the kinetic energy vf5. nbe6zt0hukxwe g.*k9l/becomes

  12.33: A solid, uniform sphere rolls without slipping on a- ko +.(barsl-xdk8fu1srs+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 inertiel-r8v o*0 k0x8cjo wu7f;m nja $0.5mr^{2}$ . 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 -me fwqz46/tsand radius R. Each -eq zwfm/6t4sobject begins 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 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 unifot9 +05ez esc qvtjz 77tqq0b,crm solid disk and an 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 fri,0beqzj5zv ec 7ctqt+7 0st9qction 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 inclined plane.j wmjc3 r7w96sn as9z7 Which one of the following choiz3sm 9 nw7as7w6jrcj9 ces 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 ifn tbz8,l1 *7svishp1s pivoted about its left end. It is released from an angle θabove ttp,8vsi1l1b *nhsz7 fhe 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 length a0 d0p m8vj 4czj2mqj9ej7 nw/djs/x4L is fixed to rotate about a frictionless pivot located L/3 from one end. The rod is released from rest incrementmjdpxce 4jna4wmqvj/2 z0 90/s jjd7 8ally 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 center of mass?

  16.50: A uniform stick of mass M and leng:-i*(bkpcb( vw6y uai th L is fixed to rotate about a frictionless pivot located L/3 from one end. The stick is released from rest incrementally away from being perfectly vertical, resultinb*(kcy ab ui6 v-(pwi:g 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 cylindu 5 gn:f)qeg2rmg*lu 5ers with equal radii on the end of his finger: gm5lfr g*unu:ge 5) 2q
• 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, havh7o- dxn5 cvuk-z+gd 8e 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 rotate aboude la42mlk2 kaf 6:g .dywllr ).z60uyt an axis 02.dafdw4.lkrl :)eu6amgk 2 6lzyyl fixed 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, Xg*v m z5was ilir8f918 and Y, have equal masses M but different radii such arg iz*5wmf s1 89lv8ithat $r_x< r_y$. 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 anamnn z(;e*y;:yomo j9d radius R is pulled by a horizontal force F actinge o *m n(a:oj;n;zyy9m
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 cll6 wob ek/esilwu++ 27ockwise about its center with an angul6ew+k/wl+suoeb l 2i7ar 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 *f t *p+ clp9f ,w*2hihfyqpo.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 releaseti,h ffp 2*ph p*+y *l9cqw.fod, 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 turningj*ae pir**m/l6 la7 xl in a clock wise direction with respect to the pilot. T lxl*/**6pliamre7jahe 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.