12.43: Several forces act on a rigid body. If the resultant z6q gnz4j3lmp l5(m-ifnvn ,6(net) force on the body is zero, v,nmfp6z(i3 4n56zl-lm nq gj which one of the following statements must be true?

  97.39: A cylinder free to turnaround a fixed axiw r yu.1-vdb;u89y8aoim ls9+optg5ts has a string wrapped around it as shown to the right. The string is pulled with a force F equal to the cylinders weight. What is the acceleration of the strinl btroi.;5y v+uogd9 sp91 88ymtu-aw g?

  16.16: A uniform stick iau*b3rtsaz(c b +9r: cs fixed to rotate about an axis through its center. The stick starts fr(39r auc abc* srb:tz+om 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 -lzu p *c* +k,:n tbirgbe2;-s;npqrowith constant angular velocity. When the angular velocity is reduced to one-third, the kine,ziqob*s-g +b;*u2n e:-crkn rlpp;ttic energy becomes

  12.33: A solid, uniform spyax9n, tcx3; xw; lp+ihere 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 has mass m, radius r, and (u 3nydw* yy9srotational 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 uniform ring(ecjxb)te7u9i8: a 3e n igzgvx6w2c8 each have mass M and radius R. Eu(:xa cg9ie8ebwjt)2vn ie7c 6xg8z3 ach object 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 uniform solid disk and an ideal uniform ring each have mass M e5p- 41vbar su;k3f w n4w/uhrand radius R. Each object begins purely rolling without npsb uuw51 fr vkar;/he-43w 4slipping 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 inclined pl 5)/ nw jup:h86qsn 0y2hy2snacmau 6sane. Which one of the following choices best rs a puwa0h2nny 8j)ys5:mcnu6hs62 /qepresents 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 i5w sjp8dn w:u+ odm9*os released from an angle θabove the horizontal. Wh5:jo dw9+*onwupm s8 dat 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 L is fixed to rotate about a frictionn zsag0eq p+*9qo/q8l a+ucw 1less pivot located L/3 from one end. The rod is releaseqa+luqgwcnz*91 qp e80+ aso/d 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 center of mass?

  16.50: A uniform stick of mass M and length L is fixed to rotate about a fee fu5 g;3,ysxtn5 su6rictionless 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 axn t;e, u3f6s5guyse5 bout 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 ea8wv zwapx4:2d+hv* w edcq/b 9ch of three long uniform cylinders with equal radii on the end of his cw9: be8 wha42v+dxqzdpw/*v 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 massestj0 /98b se7v2q dp ;aat9frmc $m_x$<$m_y$, 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 ac3)0r5k-*a -utwk/d csj ws.yh cn0zire mounted to rotate about an axis fixed through the ceak -si0k /z r5w c3.ccu*j0t sdwh-ny)nter 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, X and Yb. hu2.ng4l *xftu6v n, have equal masses M but different radii such tlf 4n62* v.hnubtu.xghat $r_x< r_y$. 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 radiuijat sqbtdtrw;0550 , e81spxs R is pulled by a horizontal force F acting t1xj a0t ie5r,5w p;sq0dbst8
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 5lljrm*c,l ta(u3 )mk radius R rotates clockwise about its center with an angular speed lkam m(ut3ljc5),*lr $ω_0$ . 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 ; bij v2hm.x s(4h x4m4 p7kdrvm40jczh5-sbnkg and radius R=10.0 cm is connected about an axis through the center of the cylinder to a horizontal spring with spri(07 bvj4b -xjphmsv4hs 4 k;mdx5m4zn. 2richng 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 l()rjnoa 2 8 p/. j:7oexrpkuuengine 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 which direction as the pilooljx p(ue: or72ra./pn)k8ju t tries to make a sharp lefthand turn.