12.43: Several forces act on a rigid bodg/juj/igd + 7iy. If the resultant (net) force on the body is zero, which one of the following statements muj /ug/g j+id7ist be true?

  97.39: A cylinder free to turnaround a fixed axis has bi(/h:rozcq,nl6 23,jp ivsn 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 acchp3,c(iqnzl2v s:/on ij, 6 breleration of the string?

  16.16: A uniform stick is fixed to rotate about anvln+ *8xvrom6thg5 * a axis through its center. The stick starts fmr xl* *gnavh5t6v o8+rom 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 constann pft/pg +m 1qo1aym uctf*:3:hx3.iet angular velocity. When thee q+1fcy g:mn.: tp*p33uo1amit x/hf angular velocity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls withoutczaqy 8ffked 11;)u k, 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 rotational inemp9hf t1157m,kfk) ls 6qhquhrtia $0.5mr^{2}$ . 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 s3q 0hos*tffmt*b(+in. j p8o iolid disk and an ideal uniform ring each have mass M and radius R. Each objecp3miq i(s o jnh8ot.0fbtf*+*t 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 i+8vdv;)w(suihn9coso )* /)u mrx2dkjnbn 5 and radius R. Each object begins purely rolling without slipping do ix w9j c ;u/n(o)5mi)vdvr+u)bs n8*odhs nk2wn 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 plan 1h,v+ z7:k7 tnzbvprle. Which one of tpbl z k7,1+r7 :hnvzvthe 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 aboutjvh+y9,j8 pnltg)fr6 its left end. It is released from an angle θabove the horizontal. What is the magnitude of the angular acceleration of the rod about the pivot when the rod isnf gth, )6l +jpj9yrv8 released?

  15.46: A uniform rod of mass .h 0 lp( ,gofj7galsn+M and length L is fixed to rotate about a frictionless pivot located L/3 from one end. The rod is released fromna l0+s(7 pg.ohl,f gj 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 m3 jg4j2kymi; iass 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 vertical, remjyj i ig4k3;2sulting 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 cylinderj,e dvol, (sa3y go*g8:8 xgacs with ( g, gsae8*ca3xo8:gvlodj,yequal 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 disks,X andY, have masses8;wn+tu3rocnv/c v 9-0 ruhu n $m_x$<$m_y$, 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 eq70q 3zpgg yv:2bs,0 -iwrhqvyual mass each are mounted to rotate about an axis fixed through the cente-3sziwyvrvh 200,b7: ygpgqq r 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 Y, have equal masses M but different radii imjjyqk.cwb.xzoqw;ll,) qq( 8h 91;such tc )ko l ji9w8.zm(b ql;xyjq;., hwqq1hat $r_x< r_y$. 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 wjl upwa3:z/7.us1s8j44wopr nqw ug1ith a mass M and radius R is pulled by a horizon.wr l: nwaou3guw / 8pzus jpjs17q144tal force 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 masqkbtdm) -l-.w6uf jg-s M and radius R rotates clockwise about its center with 6 qg)fkt--bjldm.wu- 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 solidhr.,l8myp m.ctwgm1 wh95 zf)tc h2)o cylinder of mass M=2.00 kg and 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 f,g wc1y8.mm lo))c59rw2tzm. tfhhhp rom 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, szmfis53t1 r 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 in which direction as the pilot tries to make a sharp lefth3 mr,si5zt1fsand turn.