12.43: Several forces act on a rigid body. If the resultant (net) force on thxxs6l oua6 o5744wtlhe body is zero, which one of the following statet4w7 xh5ll6o6asx 4ouments must be true?

  97.39: A cylinder free to 1/ndpakl vc1 fz gf;i n*w7c)j5pr7m 0turnaround a fixed axis has a string wrapped around it as shown to the right. The string is pulled with a force F equal to the cylinders weight. What is the acceleration okc 1nvgz7fl 7dj1;af5i/0c* prpw m) nf the string?

  16.16: A uniform stick is fixed ueyuz f a9+7rby( im71to rotate about an axis through its center. The stick starts from rest 7+mu 7ry z1ea i9yuf(band 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 hasczu.f d1v,:ru asoog2 xe7 b07st.bn7 kinetic energy K when rotating with constant angular velocity. When the angular velocity is reduced to one-third, the kinetic energ. eobvcu2n bt o,0f1:7gur .xz7ssd7a y becomes

  12.33: A solid, uniform sphere roll8azu:ymh g)t 8 p:y) ohqv.v/js 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, and rotap mkn5dhl0c3,9 cql;x tional 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 disx6yfwrg0s )7 qk 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 friction for the disk sq r0xy w6g7f)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 ideazv4 g*g*l4wx / vi4nsol uniform ring each have mass M and radius R. Each object begi*vg *w/zlgs4vo x4ni 4ns purely 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 without slipping on a rough inclined plane. Whrfi. j-qi5cvi) 2nut.o 4 h9wsich one of the following choices best represes nfhc jvi4o9tu iwq) -.r25i.nts 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 about its left end. It sui dxoj-;j h.n;;yg(*hha 6his released from an anhh;x6gonj y sd hh;a;(-*iuj. gle θabove the horizontal. What is the magnitude of the angular acceleration of the rod about the pivot when the rod is released?

  15.46: A uniform rod of mass M an2 -czdqp 0l(j gwvk8;ld length L is fixed to rotate about a frictionless pivot located L/;k 8v2 0jlq(l- pgdwzc3 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 tl+ /kr7,kzkt9lvb9r 6h c+lapo 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 stick is horizontal, what is the tangential speed of the centl6 +9cl vhk, rp9+t7rkk zal/ber of mass about the pivot?

  06.24: A person tries to balance vertically eb sjc g(i9 l5biaeik2j9 n8p62ach of three long uniform cylinders with equal radii ibjei 2jkg(5l8b s9anc6i p92on 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 andY,qsl h.los/bed, 4zi 7( 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 abqwuf30k* x2l.mhjv .eu+myt +out an axis fixed through the center ofhkmvm03+ u..f* xuqewt2+jly 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 diue 2d4csv(5fv bt *mx4sks, X and Y, have equal masses M but different radii such 5bvs44edtv* m(u c2fx 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 with a b-3azn -5zcmpmass M and radius R is pulled by a horizonb czm3pz -5a-ntal 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 mass M and radius R rodye1938qq 6 ;i .+o+5 ujylu adlowxfrtates clockwise about its center with an angular speedrdj+ 8 ;yiow 39 d. 6yqqlo5la1euxf+u $ω_0$ . 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 masnjmo ny+7 l)1 ,2z .zlsgvla4vb +u5ros M=2.00 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 +nv.5l1+ ablo),yj z uo4 rg7sv2 nzmlcylinder 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 si f 0uc3;ro)r.h2gvwyqm8mk +kv c 42wbngle engine plane are turning in a clock wise direction with respect to the pilot. Th qy08b;f2h gwcwk+)23mu 4.rmv vcorke gyroscopic action of the moving parts will cause the plane to move in which direction as the pilot tries to make a sharp lefthand turn.