12.43: Several forces act 5r75ekibt9pne)ud-lblmv5 t l*l (me-1e7 awon a rigid body. If the resultant (net) force on the body is zero, which )te15( 5e v-adrmnllu7we k5lm7i*eb-t lp 9 bone of the following statements must be true?

  97.39: A cylinder free to turnaround a fixed axis has a string wrapped arouncg i5b 2g77pdwd it as shown to the right. The string is pulled with a force F equal to the cylinders weight. What is t77 gd2 wgcib5phe acceleration of the string?

  16.16: A uniform stick is fixed to r71+gyk zmwq, dotate about an axis through its center. The stick starts from rest and rotates through an angm71+ qkwyzg d,le 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 wiu wkzn;r6phh ok):u) 9th constant angular velocity. When the angular velocity is rehu;znk6)kho:pru9) w duced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slipping on a floor alo 1y-r 9qhf*bk.ssa/dhng 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 rou9f*r7 z khui6ci+cmjoi2gg (,zai7 -tational 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 difnu8c*y 8l:l+y-jq, sysy5,hc4t auru :bob(sk and an ideal uniform ring each have mass M and radius R. Each object bbn yu5 yubhy884aorts, -cyl j cu(,:s*l+q:fegins 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 M0ufpgt l.bu:4o dbi38 andd3 f.pg:otbl0i4u8u b radius 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 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 pla6nl/ /h hw0 qj 9ndchj2sl64tbne. Which one of the following choices best represents the type and direction6t l4n/2dnh j/ch09 h 6slbqjw of friction (if any) acting on the cylinder as it rolls up the incline?

  14.43: A long rod of length L is ;m jf gvow 6the6a.i/ri) 7e3upivoted about 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 is fvuei / mgje a7) ;6tr6.woi3hreleased?

  15.46: A uniform rod of mass M and length L is fixo jixm;*j 8f 3exj),u j(d.l ju:1s0u o2mzpjxed to rotate about a frictionless pivot located L/3 from one end. The rod is released from rest incrementally away from being perfectly ver sojl8px jj.1x) 0z:jiuf*;2j (ju3m,euxmdotical, 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 fihuzkdq-,t s+duh- b,0n.y2 6yxx 3c kgxed to rotate about a frictionless pivot located L/3 from one end. The stick is released f3 n0yh-yxkub6hc,+d ,tzu.s -k xg2 qdrom 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 vertically -ebo g,/upx 1zw* /eioeach of three long uniform cylindersp/iz ,e*-gbxwo o/e1u with 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, haver8iwgypp4i8kq am 0/ary.z bnrv;:1 6 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 uniforf4z1 al(lxxd8f9kgy, m disks of equal mass each are mounted to rotate about an a xl 1k,(ag48yfzdl x9fxis fixed through the center 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 disks1haq o:8qwn ug (7ufrh25do 1w, X and Y, have equal masses M but different radii such th1uoqqha wo 2dwfng 185u:h( r7at $r_x< r_y$. 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 radiu) on nd ;f6y5w8skbyt0s R is pulled by a horizontal force F acb;0ontnkyw 5 8dy 6)sfting
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 andp4*mvl3 **9wvwu umdi zy y(e6 radius R rotates clockwise about its center wz 4uydw*vu( i*emw6mpv*l 9y 3ith 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 cyr tmcck h8zvebml429qe k): ;0linder 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 from equilibrium. When released, the cylinder rolls without slipping. Wha tbk98:cl0 v)rcee;qm4km z 2ht is the speed of the center of the cylinder when it returns to equilibrium?

  01.39: Suppose the en5t hb1,o1dfuc)fc tk3)w:y8n 7+tq. ecm e kengine 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 cause the plane to move in )btc.u,qwk1+c) e emfcnd1 o e578:tyknfth3which direction as the pilot tries to make a sharp lefthand turn.