12.43: Several forces act +rjb).)+r sxl,w egibon a rigid body. If the resultant (net) force on the body is zero, which one of the following statements must s. ) l,xb+)+rbgj reiwbe true?

  97.39: A cylinder free to turnaround a fixed axis has a string wrapped ars rr)x9q 07dp*3hxf l p/:tmwqound it as shown to the right. The string is pulled with a force F equal to the 9xf7r3:hs)/xm0wq qltprd *pcylinders weight. What is the acceleration of the string?

  16.16: A uniform stick is fixed to rotate about an axis throu+;w)6*( mmqwik izk hjgh its center. The stic; )hkwm +6ikq*(ijmzwk starts 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 g7 74e :0my)aywi/ovxr v i+cdkinetic energy K when rotating with constant angular velocity. When the angular velocity is reduced to one-third, the kinvicr ow)agdx 0 4/:v7ei+7myy etic energy becomes

  12.33: A solid, uniform sphere rolrr1p,4l vhmp5+1fqi xp *uf+dls without 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 rotawt4d(t: r 0vhdtional 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 have mae8)d c(gjjif;(xa l 9bss M and radius R. Each object begins purely rolling withoutl9cda (8x b)j;e f(ijg 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 anp0p p2 rm d+/+kt0dx,hj w ac+:*qpbxrd 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+cd+wp xb p/:+2am*t, prxjhk 0r0d qp 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 routp- iqgf:rh 0s,h1z 9 ol0lt5agh inclined plane. Which one of the following choices best represents the type and direction of frip5t-ztql 0lh1sfh9iga0 ro: , ction (if any) acting on the cylinder as it rolls up the incline?

  14.43: A long rod of length L ,twxf rbdt *biqx1538, yxx k*g*+0pju ute3o is pivoted about its left end. It is released from aj,xu u ewdrt1kiox0*8*f x35yq,+ btb3 *ptgxn 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 nvv 7fua f( y**vdsb17L is fixed to rotate about a frictionless pivot located L/3 from o(f *bvn vu71y7a fsd*vne 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 acceleration of its center of mass?

  16.50: A uniform stick of mass M and length L is fixed to rotate about awlrl8k s;bf(, frictionless pivot located L/3 from one end. The stick is released from restl(bl ;k8fr ,ws 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 uniform cylinders+3i lewsync 0qpyz:./ with equal radii on the end of his finger: w:zl+q0y3c.n p se/yi
• 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 agy :n )9+slunvndY, 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 uniform disks of equal mass each are mounteu 8h7xwwq sv.-d to rotate about an axis fixed through the center of the disk. Each disk is78h -v.uwsxqw 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 0b6n6qexci2 mn 2h 5irmasses M but different radii such t eni562xnqh26 ir0cbm hat $r_x< r_y$. 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 masi2h0k 0v ljw1ss M and radius R is pulled by a horizontal forchl0i1 j2ksv0 we 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 clockwr1 ir-8dsy 9heise about its center with an rh-edy8i1rs 9 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 kg and radius R=10.0 cm is gduh*hzm50l(.2u4nww5e,e tqv8nw k connected about an axis through the center of the cylinder to a horizontal spring with spring constant 4.00 N/m. The cylinder is pulletqv.w2d lmg8 *0, n5ewewu4(n5 hukhz d 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 engiawy35jrw )8 qcz7 l,bw+6bhtine and propeller of a single engine plane are turning in a clock wise direction with respect to the pilot. The gyroscopic action of th,wl)w 3hqy7b8+zj6ar ibc w5te moving parts will cause the plane to move in which direction as the pilot tries to make a sharp lefthand turn.