12.43: Several forces act on a rigid body. If tbxrx0 ;m)7ww b+(osvn he resultant (net) force on the body isxx)mw(rn0wbso7+ bv ; zero, which one of the following statements must be true?

  97.39: A cylinder free to turnaround a f hxfpm tekbw6ut2a9 r*4j 9g(e4 :ljf-ixed axis has a string wrapped around it as shown to the right. The string is pulled with a force F equal to the cylinders weight. 9 r*pt4g kb6x wjfe-2 4hl:ua9ejf(tmWhat is the acceleration of the string?

  16.16: A uniform stick is fixpbj/r-qr 4zx; f 4zql8ed to rotate about an axis through its center. The stick starts from rest and rotates through a4-lq fr/8xjb z z;4rqpn 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 g2a1/m(uvs pl has kinetic energy K when rotating with constant angular velocity. When the angular velocity is reduced to one-third, thealum/v1(2 pgs kinetic energy becomes

  12.33: A solid, uniform sphere rolls y s2c, fpt*.drjg:d 4j9pg/jtwithout 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 mas.qge+2bcm/.l sp1r g vk, vr8s4phuu)s m, radius 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 unifip) 5m63 mqh;0ppmn qhorm solid 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 with the i 0 p56mhp;3 h)mqqpminncline 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 unifo ks+1yzomj,0 ja7 i0 aia8c)zxrm 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 0 8i )0 jacs+xamyjizokza1,7 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 ro/,x x6akluht/bh,o +m lls without slipping on a rough inclined plane. Which one of the following choices best represenm/x hlhua+ktob,x6 /, ts 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 L is piv5rmhsbg1* uy6jm(wu2bs d7 j rty4* (xoted about its left end. It is released from an d215bb6jghy*x( tsu4sm7 ( ywmur j r*angle θabove the horizontal. What is 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 L is fixed to rotate about a fricti1 kzn98 zzf8syonless pivot located L/3 from one end. The rod is released from rest incrementally away from being perfectly vertical, resulting in the rod rosfyk88 z91n zztating 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 jmsif,hbfvim,9*u(l j) 4v (v mass M and 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 hor(4u9isvi*j)l,(f vm,vbmh j f izontal, what is the tangential speed of the center of mass about the pivot?

  06.24: A person tries to balance verti1 m65yu)1orv *hkkvyv cally each of three long uniform cylinders with equal radii on the end of his fivkuky 65v1y1orv m)h*nger:
• 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, h-p wwpe h.dg24ave 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 uniform disks of6:oxdfnr58v3a hr ve:az,nx 2 equal mass each are mounted to rotate about an axis fixed through the center of the disk. Each disk is initially at rest. The radiifx:n 5rxdhv83 nzavo :,r2ae6 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 c b dtq5yq1xo9+apq09equal masses M but different radii such thxq+ya0bqo9 5c tdq 19pat $r_x< r_y$. 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 cylinderk6q - xsteuw37n+ z,mz with a mass M and radius R is pulled by a horizontal force F ak+x7qz ,m 63-zwtnusecting
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 about ix m9em7 ycsm7*ts center with an angular spey 79cmmm s7ex*ed $ω_0$ . 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 radi lsqc,8iy8v6sus R=10.0 cm is connected about an axis through the center of the cylind,iycl68v sq8ser 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 it returns to equilibrium?

  01.39: Suppose the engine and propeller of a singl0 tm ug2( am6dv c1ixys9.ec(ul;yl7 le 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 td(c2 ucymi y gt .;elm(xv0l1l9a6us 7o move in which direction as the pilot tries to make a sharp lefthand turn.