12.43: Several forces act on a r/kqxo4 c)uo97l doia *2.fyahigid body. If the resultant (net) force on the body is zero, which one of the f a*u.i7dkooqal/9)f4 o2xc yhollowing statements must be true?

  97.39: A cylinder free to turnaround a fipofwy /-,n 7obxed axis has a string wrapped around it as shown to the,7/w -oyob nfp 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 ax ,:3 aa1vr-x fw*sjohfis through its center. The stick starts from rest r, ja13ow:*xvhaf- fsand 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 q*,bglp dl5b6h2jqs1 lrkc-8has kinetic energy K when rotating with constant angular velocity. When the angular velocity k8l -126 g,*plqqr5h blsbcjd is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slipping on a fk ) qya9i3c5nfb st42sloor 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, ub ( .z. hjcp2/av zu,4ldw6suand 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 uniform solid disk and an ideal unimtcby4.b 67e wform ring each have mass M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. The coefficientsewbbm.6 7t yc4 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 haucuu0 ,zio p y*l2t5+zve mass M and radius R. Each object begins cz20u5 *uytpo z+,ui lpurely 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 witpi+o1sm4ydf , - vxjm(e9-yp ehout slipping on a rough inclined plane. Which one of the following choices best represents the type and direction of friction (if any) acting on the cylindedim9 y o 4f-exe (vp1+sp-j,myr as it rolls up the incline?

  14.43: A long rod of length L is pikf(xrz 3co urjaoz8x4l f4 /,8voted about its left end. It is released from an angle θabove the horizontal. What is the magnlo rx4ku/384j xzra8,(o zc ffitude 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 aboue3c x/h(ilxge ns8:b1t 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 clock:1gxshieen3(l 8bx /cwise 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 a fro 8d)kbq yzi 0 )yx20;pom2tkfictionless pivot located L/3 from ob0ytyx) kfd mz)2 2q0k;8opione 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 of mass about the pivot?

  06.24: A person tries to balance vertically each of three lo) 8s wziq mje2.gr*:fzng uniform cylinders with equal radii on the end of his finw 8rm)z fzeq.gj:i2s*ger:
• 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 dis/4 zn1e k* kkk lkky7d v55u,r1g:vtmrks,X andY, 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 mounted to rotate abqtvbga8:m1:lde 4 m(k .pkae-out an axis fixed thtv. akbd8q -a4e (1: :mklgmeprough 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 disks, iva v ,(-n+s oxa(j.glX and Y, have equal masses M but different radii such ,gl+v(inx.-(oa vsa j that $r_x< r_y$. 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 r sxo+8oxl4p fya+w(3 with a mass M and radius R is pulled by a horizontal force F aco8o x p aw+f+4(xryls3ting
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 clockwiseb)d8ze3f o0w c about its center with an angwc e d0fb)83ozular 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 isza *e,6m8i1, mg-lk cjk, qdyw 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 cylik aj,dikq,g m ec,-16zmy l*w8nder 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 single engine plane are ture ;j j71awwmrq8vf83i ning 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 make a 1 ;8majr7w8veijf3wqsharp lefthand turn.