12.43: Several forces act on a rigid body. If the resultant (net) force ov+s.ve536owrnm jn)vqi- sf 2n the body is zero, which one of the following statements must3m s6 rnis+ v n-f5vqj2wv).oe be true?

  97.39: A cylinder free to turnaround *xwwn-vn*f,i5u.w9c jt aw v hdqa: 80a fixed axis has a string wrapped around it as shown to the right. The string is pulled with a force F equal to tht a, - van.9d085vw:x*wncwjhqi wf *ue cylinders weight. What is the acceleration of the string?

  16.16: A uniform stick is fixed to rotate about92 pl;y hk3tec an axis through its center. The stick starts from rest and rotates through an angkpl;hy3e t29 cle 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 fax9ig:t4paopjh:3n o ab- z8 3en blade has kinetic energy K when rotating with constant angular velocity. When the angular velocity is i3-zb39gj o:ao p4x:h8t eapnreduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slipping on a floo2 xan*xc-w5*;i u cvxar 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 rotational ir meu hlx85lu, tk)6r:nertia $0.5mr^{2}$ . 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 andab m9 ffil4d/asd(;ml8*/ l ed an ideal uniform ring each have mass M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. The coeffici/ sdm *lim(dll48af bf/;9adeents 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 have massdxayu1ng j ,r05ck 41s M and radius R. Each object begins purely roa54,k0j1sc uy1g ndrxlling 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 without s 9mhdcwyu23 6dlipping on a rough inclined plane. Which one of the following choices best represents the type a 3umy 6dhd92wcnd 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 atk6hha j)0,n cbout its left end. It is released from an angle θabove the horizontal. What is the magnitude of the angular accelerata hjnt)c6,h 0kion 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 abo53 xj .4zmtudtab ckmv e8:+4qut 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 is horizontal, what is the magnitude of the tangential acceleration of its center o.4dxutjta:zq+3k e mb c4 5mv8f mass?

  16.50: A uniform stick of mass l.i(90oiak ypn(*xng ;czrj / M and length L is fixed to rotate about a frictionless pivot located L/3 from one nalj/*ip0o (xr( z.k cg i;y9nend. 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 triesh mi2tk((exb0wjqi30b he1(e cf0 0tt to balance vertically each of three long uniform cylinders with equal radiie3x tke12mij00tqw i 0h(b ebf0( cht( 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 dicfijks); q:e;01tcgb: cl5aa sks,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 arekh9o v8e,jo8 e mounted to rotate about an axis fixed through the center of the8ho8 jv, keoe9 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, X and 4:k 6mqqccz w:er..ljY, have equal masses M but different radii such tcwe.r 6l4j .zm k::qcqhat $r_x< r_y$. 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 ranz iq-53p tdsa*e ,/medius R is pulled by a horizonm,ip/zt 35neeq -sd a*tal 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 ma*1ogvj h01 gkdss M and radius R rotates clockwise about its center with an v og hd0kj11g*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=l8cv +nt4a1 4ztq cj9s2.00 kg and radius R=10.0 cm is 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, tqt j+z 1vl94c4atcns8 he cylinder rolls without slipping. What is the speed of the center of the cylinder when it returns to equilibrium?

  01.39: Suppose the en 16 qui(no2u4v*uhxjlgine and propeller of a single 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 thi4xl1o6qvj 2u u*uh (ne pilot tries to make a sharp lefthand turn.