12.43: Several forces act on a j 4nx1 oixlmy6*g0/hf rigid body. If the resultant (net) force on the body is zero, which one of the following stgm4 x0o1lx6*fnji /yhatements must be true?

  97.39: A cylinder free to t9cmw6)j w ul9ywijq 8)urnaround a fixed axis has a string wrapped around it as shown to the right. The string is pullew8l uqij9 w)9 wj)ymc6d with a force F equal to the cylinders weight. What is the acceleration of the string?

  16.16: A uniform stick is fixedz rx6a2pr u)a: to rotate about an axis through its center. The stick starts from rest and rot xr:u6z )arap2ates 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 kine;2dc +w cvsgo tqy7h79.we4gvtic energy K when rotating with constant angularhe sgqvdgwo c; t.7wyc24 +79v velocity. When the angular velocity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls wit5 oiseojvcxs*o; 1xh y5g-3:i hout 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 rotational ie6ok cc1tn35cgp j remw; 3;5wnertia $0.5mr^{2}$ . 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 eapay6okc u::h)k /olaa t.j15 fch have mass M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. The coefficients of fricti.oyau/k a:of a1kh6pj)c: lt5on 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 dpg5jgvq*gb2,m id1 f i4+1xqc/ 9agt tisk and an ideal uniform ring each have mass M and radius R. Each object begins purely rolling without slipping down a robficq vdg9t1pq4,agx /tg mg j 21i5*+ugh 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 roughbbk:fa-y(kh t. l/xl m*foe(0 inclined plane. Which one of the following choices best represents the type and direction of friction (if any) acting on the cylinder as it rolls up th k .a l(-f:m(hxlk ot*feybb0/e incline?

  14.43: A long rod of fax;usu,c1p9length L is pivoted about its left end. It is released from an angle θabove the horizontal. What is the magnitude of the angular acceleration of the rod about the pivot when thf u9p uxs,1c;ae rod is released?

  15.46: A uniform rod of mass M and length L is fixed to rotate about a sdwcu q8j00x s31i2 eudbdl88frictionless pivot located L/3 from one end. The rod is released from rest incrementall8l 0 88b2eu d iddqwcss3ujx01y 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 fg :j)4eq8) mq yfkg/yovw(wq3ixed to rotate about a frictionless pivot located L/3 from one end. The stick is released from rest incrementally away from being perfectly vertical, resulting in the stick rotating clockwise about its pivot. When the stic348qy)fo :vq/gyj wwgeqk) m(k 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 ysg49p )4mrq jmjucf6 ox.zlgo-- 0h. uniform cylinders with equal radii on the end of his-)4 jo.90f mqjghu r6xpo.mg lzc4y- s 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 andY, have mas fn+ /mvho 12avwcof73lad3( gses $m_x$<$m_y$, 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 about l8 xi-vj4rcm* c)mn1 -quhjl0an axis fixed through the center of the disk. Each disk is initially at rest. The radii of the diskmx4mu- 8nr0)c j*cilh-lq1jvs 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 masses M bz7w20jvz r3gqut different radii such that wj7vqz 20grz3$r_x< r_y$. 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 is pulled by s;7l wvs-51vuaxxu h 6 ut,g:la horizontal force F acti5us;7wgu ah-l: tvx6u1,sxvl ng
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 ovd-0f g; rshd;: n;.yb gp7nv2a oma8bf mass M and radius R rotates clockwise about its center with an anga7dnahg8 dpvs gm-;vbyb2.fo ;n; r0 :ular 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=1 jabovq3z,waef *b ek: l3-(3j0.0 cm is connected about an axis through the cee ba-v: 3j3f3wkoz(*,lbeqj anter 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 engs e(qix w1ru69 3,aqxaine 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 d6w1, raq iaqxexs3u(9 irection as the pilot tries to make a sharp lefthand turn.