12.43: Several forces act on a rigid body. If the ab v6wooig8 t2 -5kszn9 xxr0/resultant (net) force on the body is zero, which one of gstoxoin2 /608 rxbva9-wkz5 the following statements must be true?

  97.39: A cylinder free to turnaround a fixed axis has a str:xr;-cmo k1is ing wrapped around it as shown to the right. Th1 k;s m:oci-xre 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. Tf39ocwm(t9 vfr -jki:m g.3krhe stick smjff( .c-rvwi9kt9m k3 r3:gotarts 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 blade9ox yqhw8-d9p has kinetic energy K when rotating with constant angular velocity. When the angular velocity is reduced to one-third, the kinetic energy becomowq9h98y-p dx es

  12.33: A solid, uniform sphere rolls without slipping on ab25.ar jzz,;c00 l0 tqte5oo lgbt 0qo 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,v wjx( nd,a2bd o(i(i) 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 unifi45x zalmzz0p)zt z8p+ ;8utform 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 w8i) ttax;u5z0zp4m z8z zpl+fith 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 9 7xyi(ml -6 f9+cjkov4 lrkk;gqfow 0uniform ring each have mass M and radius R. Each object begins purely rolling withou+f(o9ykfkq4l0x769 gmwio c ; lv-kjrt 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 roug1 yvl1psszf:vn. l*u8h inclined plane. Which sfpy.8*lzu svl 1nv:1one of 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 its left end. It is relea0 ob.vg14x5gkbdh * resed from an angle θabove the horizontal. What is the magnitude of thg bg* x.01hkv5de4 robe angular acceleration of the rod about the pivot when the rod is released?

  15.46: A uniform rod of mass ;e87a3yttlc. 3w q njxM 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 rot.nel wjqat;tx 7c3y 38ating 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:lt;:z h qs.y ur.hsq+d 5jl6xm1yc:fyrk 2r5 fixed to rotate about a frictionless pivot located L/3 from one end. The lsclzmr y6jkx;+:yytr5 1q2f5s: hr . qh: du. 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 bloiw.ur/c j+z2 a-+zc q+dr; zalance vertically each of three long uniform cylinders wit ++q; dczair2lrw o+/z j-u.czh equal radii on 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 dp6ix:usu+(w mz uf7; ylwnq .4isks,X andY, 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 equalgscdz1n45rsh/ +/s kciyi0t 1 mass each are mounted to rotate about an axis fixed through the center of the disk. Each disk is init40 1/r/cscn1 y+it5ssgkdzi hially 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 dibpmux h( yck2xgjj:9j5x. -. w3wd)sifferent radii such tha x.(ps-k:i3 2jhuxcw xg.)5bjy9mdwj t $r_x< r_y$. 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 b w; 8hne-gxge*zy4q(cy a horizontal forcee4nwzyg(q * h gc-8;ex 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 rotates clockwise1dlai/ep /ik r e1o3)hs;mv9p about its center o9d1m3i/ r)a ie/kels; pp1hv with 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 kg and radiuxo8z2b-jpl tjv )s4;fs 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 slippinj2xs8fl o4z b; vj)tp-g. What is the speed of the center of the cylinder when it returns to equilibrium?

  01.39: Suppose the engine and propel78:zzi;7 ;y j bqw4sar nj4jaller 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 in j4 z7 is4wjz; ny:8rqaal b;j7which direction as the pilot tries to make a sharp lefthand turn.