12.43: Several forces act on a rigid body. If the resultant (net) force vi 9 3n,ic am+o619cycsmonc+ofg0g7on the body is zero, which one of the following sta9om9, o7ifaci+0sov ygn ncm c1c36g+ tements must be true?

  97.39: A cylinder free to turnaround a firlx-y:w* /* a f5fmk*qy8loir xed axis has a string wrapped around it as shown to thl-y x5f*mkyirafr/*wl8* oq : e right. The 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 aboutp *cf9bs zz,:m an axis through its center. The stick starts from rest and rotates 9pc, f: b*zmzsthrough 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 kineticwap:p gwun823*7pmduda to:. energy K when rotating with constant angular velocity. When the angular velocity is reduced to one-third, the kineticnu*pup8wtd3.7gpaa 2:o: d wm energy becomes

  12.33: A solid, uniform sphere rolls without slippidj4u)(2aw4fmf v -ssgng 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 rotationmh+otxpl mgduhxc0+r n 7l-+;jl )32+dmny0fal 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 each lym4 o74r5w1zbr+l;cg6b prg have mass M and radius R. Each object begins purely rolling without slipping down a roug lrrbgzb g4yc1o;p+w5 7rl46 mh 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 M0+rmf,m54keqz w14jjy sxs s7t px:g4 and radius R. Each object begins purely ro4s1 fr0jxs gmk: zj,5x4w+e4ymt7 qpslling 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 mp0a ag+;xza7( ex 1mnon a rough inclined plane. Which one of the following choices best represents the type ag;mxp0 +ex1a mz7( naand direction of friction (if any) acting on the cylinder as it rolls up the incline?

  14.43: A long rod of length dzeyim w5m;7 1+vcb8rL is pivoted about its left end. It is released from an angle θabove the horizontal. What is the magnitude d 87 cm+;re5w1bivzmyof 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 tom8ce;ah wxm2(* - -ihhlgehu, rotate about a frictionless pivot located L/3 from one end. The rod is released from rest incrementalgh,ahhl- m* c8 em -uh;xei(2wly 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 aba 3j2 d,2gvi/p5vin l6tz4hb frictionless pivot located L/3 f zbj6d2n/ii5 3gpat 2l4v,h bvrom 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 the pivot?

  06.24: A person tries to balance vertic dzyl, y35n-aery xf iw*k/o(o9g0s) cally each of three long uniform cylinders with equal radii on the end of,ayk signy5-*/9rlxdf)oz(0w c y eo3 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,/dwy ;*h73lg*viz l.dv,z vrb a6pmy*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 unifbncv fo zos gu6+g,).3orm disks of equal mass each are mounted to rotate about an axis fixed through the ce+ .u fcv z6n3)osb,gognter 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 Mf)cs b6/pq3es but different radii such that6 f/p )qcbse3s $r_x< r_y$. 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+p9c;/fuzv ;1pv iq- j k4kk8nuzan9 c mass M and radius R is pulled by a horizkzv9 9zcia;+uqfc8uk 1vjnpk -; n4/p ontal 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 mass M and radius R rotates clockwise ab s qh g:txdhoi2*o710nout its cenhg*d itx: q70s oon1h2ter 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 kgh:0wfrwb3 3z i.ms+kt 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 k3fi0 +h.ms3 wb:t zwrequilibrium. 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 engine plaa8q0* n2a iyrxne are turning in a clock wise direction with respect to the pilot. The gyroscopic action of the a*xny q28a ri0moving parts will cause the plane to move in which direction as the pilot tries to make a sharp lefthand turn.