12.43: Several forces act on a rigid body. If the resultant (net) force oneron 3k2yy:f r,p+rxc;nr+8o the body is zero, which one of the fony3rn8 oorpk,;cefr 2 :xr++yllowing statements must be true?

  97.39: A cylinder free to turnaround a fixed axis has a string) cfyhos-u)nxcp t3*7 ihe(k 9 wrapped around it as shown to the right.9 c(u c37-ixpohsf*ten y k)h) 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 f:2)xlh+v w 7g59(d*xqgxfc7hq ixapk,fel8 r ixed to rotate about an axis through its center. The stick starts from rest aldw *hh,fkix rc)+ xx7ex gv :(fapl9gq87q52nd 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 kineiz2lxzo9m,h1g5w v9 rtic energy K when rotating with constant angular velocity. When the angular velocity is reduced to gz9i91xhwom2 5 lv,rzone-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slippings bv xuhsb v3otdw3 6/b:vi9hdjbpd2f0)p./ 1 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 rotaticc-jyf g9)tcq -0wlf ;onal 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 3 kl7b4bdw7rq mass M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. The coeffir blwd477qk 3bcients 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 soliu 7(5ui(3mkdmpto+s:og i8e pd 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 frd ugo3ps5u(m7 o(m+et8p i:ikiction 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 ro0knda-pg p,q, z 2zxf2lls without slipping on a rough inclined plane. Which one of the following choices bzg-pzqd x a20 p,k,fn2est represents 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 pivoted aboutj8 nmwld:qxk-r11 i:2t(hmn m its left end. It is released from an angle θabove the horizontal. What is the magnitude of the angular acceleration of the rod about theim 2 m1k:8nl(dj: rwtxqh1m-n pivot when the rod is released?

  15.46: A uniform rod of mass M and length L is fixed to roty+5 ;pzk l *yknyywp9)ate about a frictionless pivot located L/3 from one end. The rp ;p+nkkz)*y9ly5y y wod 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 lengthbt 0 o1)a4g9x k o*zdfpmia:;y L is fixed to rotate about a frictionless pivot located L/3 from one end. The stick is released from rest incrementally )x4ofm* 90dz k t1;b:aoipaygaway 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 ,mzg y9tsu r/8cylinders with equal radii ,mtzu r8/9yg son 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 andbik-v4t q /u8lv;q0za sb4y x0Y, 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 uni8i2c)c5 eyyqdsbp o*4form disks of equal mass each are mounted to rotate about an axis fixed through the center of the disk. Each dicbi5s8 y2)4e ycp qo*dsk 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, X -/hjdajw5 qp7i a;ll;and Y, have equal masses M but different radii such tha 5pljhj;q7iawd/al;- t $r_x< r_y$. 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::ybsm m ce7xe(xzk5;z l50ny is pulled by a horizom zy:n ;0(l:y x c5kbse7xem5zntal force 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 maso)9249olt1 5 q+vbckdbq mg jds M and radius R rotates clockwise about its center bqjvqdk1o +d4mb )59 t92logc with 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 cylinqxv6zngp.f 0zx gq x:10pg n-5mpex8.der of mass M=2.00 kg and radius R=10.0 cm is connecxgq. z:. xxgqnpf0-g1 zmpv5 e0p86nx ted 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. 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 eng qlp+wbb*p0a23wz ;zv ine 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 whilb p+pvzw0 a3qz ;w*b2ch direction as the pilot tries to make a sharp lefthand turn.