12.43: Several forces act on a p b1fyjoj6 j80 vvubwr;)37; d2qo-afns:rwe rigid body. If the resultant (net) force on the body is zero, which one of the j r38:nj u60w;pv 7wod)oe;j1yfabqv2f-brs following statements must be true?

  97.39: A cylinder free to turnaround a fixed axis has a strings.l1 fs2,eorg j7ox -;rsq n(a wrapped around it as shown to the right. The string is pulled wigor s o,nq xasfe-rsj7 ;1.l2(th 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 a of9w8 b;blxzl:)1ky jn axis through its center. The y;wx)o 8kfb9l:lb1jzstick starts from 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 crz , 1.l fyp qg0j-x9sjgbs:5monstant angular velocity. When the angular velocity is reduced to one-third, the kinetic enmqlp5bgsz0g:sy9 r jf x- 1.j,ergy becomes

  12.33: A solid, uniform sphere rolls without sl1 bq5n gy zqu/6g:,qspipping 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 r, hq6jtahatdn103mib6()k/ zxju . (ls 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 dislo 1 ( swzv/g0/)wv;wnmg7gxlk and an ideal uniform ring each have mass M and radius R. Each object begins purely rolling without slipping down a rough inclined plannx/;w lv(1)m vzg7gg/so0lww e. 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 unifoxfo cu-8/l7/ jxvjqi45mwph k2h * s4qrm ring each have mass M and radius R. Each object begins purely rolling without slipping down a k 2/jhq4/v *4u 8lj-ihqsop5wmx fc7 xrough 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 inclined pq gq(u(t,b9lnan7dq,zqmj qa/5 ,q*t lane. Which one of the following choices best represents the type and direction of friction (if any) acting on the cylinder as it rolls n, jtl,a t,qdq *q7maqz/(gqn9(qb 5uup the incline?

  14.43: A long rod of length L is pivoted about its left end. It is released0rmzs,hd4a5cl6w *ps from an angle θabove the horizontal. What is the magnitude of the angular acceleration of the rod about the pivot when *4ap,rd s6lhm5szw 0 cthe rod is released?

  15.46: A uniform rod of mass M and9g(7c,dumiij(dal - r 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 p7iudrj9a,i ( g -lc(mderfectly 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 length L is fix1 fzka7lbtbl-8o q5lx m,/4otbsg*. r ed to rotate about a frictionless pivot 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 cente81q sz7l.5bm -ko /*t4oabt lg lrf,bxr of mass about the pivot?

  06.24: A person tries tt / viq,(cwxx ww)n6k6o balance vertically each of three long uniform cylinders with equal radii onn/xv66qi wwck) xtw, ( 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 and n,i ifo* q0rhj*arnx .9,:r3bx t:qnkY, 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 massa y lh6y*hjq.; each are mounted to rotate about an axis fixed through the center of the disk. Each .yh*a; qhj6l ydisk 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 Y, have equal masses M but differ1r)p m io:4,n.px1bddqg d4js ent radii such th)q1p x4opg4rd: 1 jsmd,d.b niat $r_x< r_y$. 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 M7olkhr 918lfu and radius R is pulled by a horizontal forcfhkll1uo9r 78e 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 radius R rot0bhanh. ot42lv8 erc4ates clockwise about its center withatcv40 n84oherb 2.lh an angular 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 t/(6dhx -exzz h rt2g4kg and radius R=10.0 cm is connected about an axis through t threzt(h62d -xx4gz/he 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 engin1d+2m e uevxod8+6eg tlt ;/cje and propeller of a single engine plane are turning in a clock wise direction with respect to the pilot. The gyroscopic action of the moving parts will cause the plane to move vut6letoj;+x2e8de+ gmc / d1in which direction as the pilot tries to make a sharp lefthand turn.