12.43: Several forces act on a rigid body. If the result-/zll*;l yf qz(,bud want (net) force on the body is zero, wdyb, lw*lqzz(; lf/- uhich one of the following statements must be true?

  97.39: A cylinder free to turnaround a fixed axis has a sd7 t0by)(e4zmzgcq s,g6 ; cevtring wrapped around it (gg; ztb64e, cvce) m70qszydas shown to the 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 about an axis through its center. (p4 +)hz)t0a veij nlpg, c)mzThe stick starts from rest a+v(0)hip,neza m)jtp 4 c)l gznd 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 consta0yrc.c i7oa+knt angular velocity. When the angular v c.i+0orcaky7elocity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slippingb1kvqlh: )t-m*,et hw 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 inertiaeu htyr+l 5b90 $0.5mr^{2}$ . 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 qcrv nh 38;7.jga75s2omm vdbsolid disk and an ideal uniform ring each have mass M and qmsdahvg;n oj c 773rb 5v.28mradius R. Each 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 eac ymil0zldkq7oye 08q) +;er +qh have mass M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. The coeff eky+oqlqm+0 de) 0zqr;7ly i8icients 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 plane. Which iwhh i:g2+ck 6one of the following choices best represent:iikh 2 h6wg+cs 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 7qtc.uqm afelh 9;rv,)*r3s c L is pivoted about its left end. It is released from an angle θabove the horizontal. What is the magnitude of the.ftuace s h9rcm),qrv;*q 3l7 angular acceleration of the rod about the pivot when the rod is released?

  15.46: A uniform rod of mass M and wh7wnzl; ibcmzxa/;/jy - 40 tlength 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 rotating clockwise about the pivot. When the rod is horizontal, what is the magnitude of the tangential acceleratijx;/wbniht /z0-m7ya;c l z4won of its center of mass?

  16.50: A uniform stick of mass M and9+t fi dnls81y 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 of81s+t i9lydnf mass about the pivot?

  06.24: A person tries to balance vertically e*69v t/rotc-a0 f alnqach of three long uniform cylinders withfa o9tr *qa-6lnt/cv0 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 disks,X andY, have massel23ps 1v,-7feiwbvi u s $m_x$<$m_y$, 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 rotate about an39g 2dn w5 mj2zkxtv4z axis fixed through the center of the disk. Each disk is initially at rest. The radii of the disks jv2n3kxztz dg2w9 4m5are $r_1 < r_2$. 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 differenwc0,4zu tk/ 7kop/bd v wp*nn3t radii such that4*d0n tknvkb /3zpwou,/7 p cw $r_x< r_y$. 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 radiu4:c.gga ou-q-hla0a -+ddp bn/gdo4fs R is pulled by a horizo- aug/0-f4pnoa-h4d: c. +o gdagdlbqntal 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 dismk5 )pfu 3pov4i7 ;fubq;t 8fkz9de7ck of mass M and radius R rotates clockwise about its 745k;3kzi 8po;ufeqt9vf c db) m 7ufpcenter 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 masx- f qq 6san(eyczpgx -78srg77t/6bdd8g rg4s 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 spring8g 8xs4 a7r-/6yz d rg-t xpdgs b67qq(fgn7ec 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 ofkn ckvgsu3:pf yw1j35f7:6 u2hesb 12u ck :wu a single engine plane are turning in a clock wise direction with respect to the pilot. The gyroscopic action of the moving parts fu:j wc7ks f1y:2un2 ks63ce h:u g5kwvpu31bwill cause the plane to move in which direction as the pilot tries to make a sharp lefthand turn.