12.43: Several forces act on a rigid body. If the resultant (net) fg5qf6w j(h se6orce on the body is zero, which one of the following stasqw 66j feh5(gtements must be true?

  97.39: A cylinder free to turnaround a fixed axis ha//(9 *aa ,oqjoradlt3 m nxf1ns a string wrapped around it as shown to the right. The string is pulled with a force F equal to the cylinla//3 *a9d o(qjn,o1amfnxrt ders weight. What is the acceleration of the string?

  16.16: A uniform stick is fixed to rotate about an axis through its cjo;,x njrz9c) ij :5czenter. The stick starts from rest ,ciz n xz:jocjj)9;5rand 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 kinetic energy K when rotating witswe13 h m:sls0h constant angular velocity. When the angular velocity is reduced to one-third, the kinm:s 1w3hs s0eletic energy becomes

  12.33: A solid, uniform sphere rq,ktfd 0zy:h+p (lr5 iolls 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, andqap og(7 dfi7afdgs g:::(8cb 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 uz (2lmoxk/5 ohas .mzo itx+l1(+zwl.niform 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 di2mszo .xz(oh.(lo+ 1am+tw xzk i5/llsk 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 soli0 fwz/t7 pwl 4p/c2mykd disk and an ideal uniform ring each have mass M and radius R. Each object begins purely rolling withotyc lwz p0k//wp4f2 m7ut 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 slipping on a rough inclined planku2 :y 6ebllt2e. Which one of the following choices best represents the type and direction of friction (if any) acting on the cyll26u y:lek2tbinder as it rolls up the incline?

  14.43: A long rod of length L is pivoted about its leo+dj)c *+c2t abuk4 qift end. It is released from an angle θabove the horizontal. What is the magnitude of the angular acceleration of the rod aboutqo j4bd+t *2)iucakc+ the pivot when the rod is released?

  15.46: A uniform rod of mass M and length L is fixed to rotate about awmsq,c84x)ii frictionless pivot located s i4iq w,m8)xcL/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 of mass?

  16.50: A uniform stick of mass M and length L is fixed to rotate about a1p7g qrq/ kx6q frictionless pivot located L/3 from one end. The stick is released fro/ q67q1 kgrxpqm 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 long un;(k a)ndly)ztw: z/b1z3y5t ;sjc tl piform cylinders with equal radii 3s z/wtldz1jtp )(azn; )ty b5; c:ylkon 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 an 7p mn(hqrh*+qk*z5msdY, 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 to3 p6 ng:il.ii(way0s b4xlm e+ rotate about an axi3 : 60giy.4iln bispealxwm+(s fixed through 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, X and Y, have equal m 6,dhxyv94ti ga*h3t 0uptgzp+bd07 hasses M but different radii such thatatg+7 z t4xi*htbh hd0vg,d 6y09u3 pp $r_x< r_y$. 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, sorc / s2cd8rs l(k9v.lrlid cylinder with a mass M and radius R is pulled by a horizontal r v2(d9k.lrc/sc8 s lrforce 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, unifo-q9tzb7n q:jgrm disk of mass M and radius R rotates clockwise about its center with an angular s njbq7gz9 qt-:peed $ω_0$ . 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 conep ze-mz vd;jo 0mr)yv3b2 ,i0nected 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, strpy0,-demb3vim r)02 vzze o;jetching 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 engine plane arerptah;n5k3j o p432pn turning in a clock wise direction with respect to the pilot. The gyroscopic action of the moving parts will cause the plane to p a;52o htn 4r3p3pnjkmove in which direction as the pilot tries to make a sharp lefthand turn.