12.43: Several forces act on a rigg uuy )8mg 16mxendmb067d z1iid body. If the resultant (net) force on the body is zero, which one of the following sme6 1m xmdyz7i08u6d)n1 gbg utatements must be true?

  97.39: A cylinder free to epzcbvci 8af;55:b z5turnaround a fixed axis has a string wrapped around it as shown to the right. The string is pulled with a force F equal to the cylindersi;a c b8:5fc vbpzz55e weight. What is the acceleration of the string?

  16.16: A uniform stick isn x.)fgz1mmj 0 fixed to rotate about an axis through its center. The stick starts from rest and rotmgz0m)1j xn. fates 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 kineticqow036 e oj rw;xm mi6sw1c5t4 energy K when rotating with constant angular velocity. When the angular veloci; smmq45 6cteww3ojw 6orix01ty is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slipping on a floor along thiw p*(evf/m2) l8q yoke $+x-axis$ (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, radi43ffz2co j/j sus 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 sou,(z7 fswln r+d;y 8zolid 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 wr(yd8;l w7u+zf zns,oith 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 uniformhcs we;s 31sn9-uh2 vz/ dus (nig)qw* ring each have mass M and radius R. Each object beginc2q);ewh (3sw s/ u szsihguv*-n 91dns 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 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 incl ( r fn8tgomosxk4rvho2)q4/9 ined plane. Which one of the following choices best represents the typr9o4ot s)4xonkrf8qm/hv2( ge 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 releagt 4n,*:8(u w iu-dwkr0 kynkhsed from an angle θabove the horizontal. What is tk(* y:uwn h g04,dikrntk8wu-he 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 frictionl9yy5rpl5 lk5c ess pivot located L/3 from one end. The rod is released from rest incrementally away from being perfectly vertical, resultkr5yyp559 l cling 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 anl,s vh 3nlo+fnha1 p+ 8f,g*grd 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, 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 t n,+v*sp ,g1a rh+ gfl3l8onhfhe pivot?

  06.24: A person tries to balance vertically each of three long uniform cyliqnd8 q0z 0kny*nders with equal radii on the end of hik *q800dq nnyzs 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 mass*fi pk2 7 9(fabiip-gc h:ven1es $m_x$<$m_y$, 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 mounted to rotat.tldbw m3n b+:)qqsn)e about an axis fixed through the center of the disk. Each disk is initially at re dn) l.nw3)btbq:+q msst. 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 butcab /*/c)m(2lrptq3hubdufbt +:,ij different radii such 2qfrb,/u :lpbtu+mh (abji)/t* c 3dcthat $r_x< r_y$. 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 with3o8o bhkaplx.m:ccw ) t g;.s8 a mass M and radius R is pulled by a horizontal force F a. b.pc3ocwa:x)h gsl88;t omkcting
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 diskck6n2a169 o8i fbowli 9k cd4l of mass M and radius R rotates clockwise about its center with an angular speed 9i c9olik4 c1 adfwol bk68n26$ω_0$ . 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=2b l/go9-w* (l htqnhc2.00 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 from equilibrium. When released, the cylinder rolls without slipping. What is the speed of the center of the cylinder when bn*lo/ t(h c ghqw-2l9it returns to equilibrium?

  01.39: Suppose the engine aoiwn ac4 ;ufe1f o g4subh.su8/,4g.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 4gc;4su/ fs.oi4gufouh .a 8wbane , 1cause the plane to move in which direction as the pilot tries to make a sharp lefthand turn.