12.43: Several forces -tllmc- ux )g5act on a rigid body. If the resultant (net) force on the body is zero, which one of the f ll-tm)u5 gxc-ollowing statements must be true?

  97.39: A cylinder free to turnaround a fixed axis has a string wrapped aroundavtsakvw 2l, 8v0+0 dr itv0rs t8v, 0ad2 +kvawl as shown to the right. 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 axis through its center. Thed 2k;zvrsk *:;w4h:jd4 tvljn stick starts from rest and rotates t;:4; v:jjlvrd*k 24zwnks dhthrough 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 rotatinq dog+ al,58mng with constant angular velocity. When the angular velocity is reduced to one-third, the kinetic ener+n dqalo ,8g5mgy becomes

  12.33: A solid, uniform sphere rolls without sliaegh *-uxlb vyomb67 ,fnl .)7pping 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 mas/1q9//du a4 skluwk d7yljja7w. vn 2js 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 sob(rcs fc2)d8f lid 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 friction for the disk and ring with the inclinedb2 ffcs)r c8( 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 masskvpig8.k iua .,qw u3* M and radius R. Each object begins purel uki*,v 8iuqk.a.p3wgy 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 without slipping on a rough inclinrge7( yp( *olled plane. Which one of the(go7l reyp l(* 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 its left end. It is reg ,au wfh9(tefnp;;j k3w 7j)eleased from an angle θabove the horizontal3 gh)k;(w ,e7aff uetnjj9;wp . What is the magnitude of the angular acceleration of the rod about the pivot when the rod is released?

  15.46: A uniform rodbfhh2, cj.*/uz rg7 aj 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 7/ha*.j 2hb,gfj z currod 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 stik. ly (+ )woml:sf5nucck of mass M and length 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 lo).kf5 (:mucw lny+svertical, 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 cylindjj/y +/0sv(jb u uiz-ters with equal radii on the end of his fingerjsu/uj( tb-0yvi /+zj :
• 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 a qpjw.ld4 3 wthmoq4/o450kffndY, 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 wjkli6)qch:s0 i )w /wmounted to rotate about an axis fixed through the center of the disk. Each disk is initially at rest. The radj kc)/:6wh0ws iiq)lwii 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 a,y82qy bcy7 +o(z 5a( kbxuwt mek+r7snd Y, have equal masses M but different radii such that +cw boyy q x7a5ms8zk7 by (urke(t2+,$r_x< r_y$. 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 cvk+au1zc 2ko hs2rajd9:-t2tylinder with a mass M and radius R is pulled by a horizontal foas +z: 22vurt hao k1dk-9ctj2rce 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 radiuqf wj*2 ;ves uc;4:mgns R rotates clockwise about its center with an angular jg* fq; ; ec4umvwsn:2speed $ω_0$ . 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 M4*hdkpkv 4nu5=2.00 kg and radius R=10.0 cm is connected about an axis through the c4*4hd pkn k5vuenter 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 p3,j2 gpxhdk tr(gepu8ev ;m:y tb(*m3lane are turning in a clock wise direction with respect to the pilot. The gyroscopic action of the moving parts will cause the r3*j,xtu2hgge:y d 8mppbv te3k;m((plane to move in which direction as the pilot tries to make a sharp lefthand turn.