12.43: Several force6*mesb , r e0lr4ecrh8frfg,5s act on a rigid body. If the resultant (net) force on the body is zero, which one of the following statements mml bgr06rrh4 ,fe fs5re,*8e cust be true?

  97.39: A cylinder free to turnaround a fixed axis has a string wrapa+*- be-ftvmisv b/ i0ped around it as shown to the right. The string is pulled with a force F*fs+ bmiite0a- v- /bv equal to the cylinders weight. What is the acceleration of the string?

  16.16: A uniform stick is fixed to rotate abo o.k3 tnfac*s2j8 dcr3ut an axis through its center. The stick stas n8t *3kcafdj23 oc.rrts from 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 jvfg .:d d*aq5v3q1hxenergy K when rotating with constant angular velocity. When the angulahgx avvd*j.5: fq3q1dr velocity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls wizfuyy t) :dl .2crw4t1thout 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 h jmz5+m ul27urotational 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 :-ooo)avw ;jz)g +qhfhave mass M and rad)oh;w jv)fzq +-ooa g:ius 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 ideqph4;n3gv (ib.,,-nqfzywl r al 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 n; nrhv-3,qw g(4lpb., iyfqzwith 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 arxb :zb yu :l5vb8o0v+k*v,cg rough inclined plane. Which one of the following choices best represents the type and direction of frictic ux0bzvk, ::l8vvbo5y* rgb+on (if any) acting on the cylinder as it rolls up the incline?

  14.43: A long rod of length L is pivo+q5nsfw1. ovlted about its left end. It is released from an angle θabove the horizontal. What is+ lwn.o1 qfs5v the 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 4t4ly l5gu xs*8cz h:3p ha hu6-zejer)8d.kw 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 6z c.h5)leze*uy:kujsp3xga84hr 4lwht8 -d is horizontal, what is the magnitude of the tangential acceleration of its center of mass?

  16.50: A uniform stick of mass M and leng3wj uzaa3 0/39 ;d-ifjlmgm bo .be7fbth L is fixed to rotate about a frictionless pivot located L/3 from one end. The stick isj3 ij bo;0d-7 a 3uwb9agmz lb3./efmf 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 vertically each of three long unfw5r-y)r4 upciform cylinders with efr )cwyu45pr- qual 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 masspl*; b gfk vv-risw)0,an/f2ep56wxees $m_x$<$m_y$, 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 equall0re4;40jw jcq0dgn ed pn:;s mass each are mounted to rotate about an axis fixed through the center of the disk. Each disk is initially at rest. The radii of the disks arew4gn4j pl;;e0q 0 r csd:ejn0d $r_1 < r_2$. 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 dr lcgdahvbrpw s 6q;l94 r4/v; nl.63lifferent radii such th66d4lvblgln9.pqr; hrva;rc l s/43 wat $r_x< r_y$. 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 radius R is p5 a)kqqh-im u*jbk ;0;mmsf z9ulled by a horizontal force F actiq) 0 mb;qas5-k* 9jmm;kfu hzing
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 c0e*hvb 7zlcxony w6.3 lockwise about its center with an angular speed .6o *0yl3z encvxw7bh$ω_0$ . 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 kg and radius R=10.0 cm is 1nfve.9goe3e;xs cm +hs d(m8 connected about an axis through the center of the cylinder to a horizontal s m c;g83 .xoe+(hne1s9dvfmespring 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 it returns to equilibrium?

  01.39: Suppose the engine and propeller of a siz*p m pq:j2a1tze*wu1ngle 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 ma *qa2z*zw1uj pepmt:1ke a sharp lefthand turn.