12.43: Several forces ac-j6icy c 0dftu480ozpt on a rigid body. If the resultant (net) force on the body is zero, which one opz6c0d- tc yjiou084 ff the following statements must be true?

  97.39: A cylinder free to turnaround a fixed axis has a string wrapped armhnyc(wmgi5 v)w a66 -ound it as shown to th-yv(w) 65acgnmi6 h mwe right. 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 fixed to rotate about an axis throug7bbq 5 p u.+0; qjgohs 5,aaoj3zo6cvph its center. The stick starts from rest and ro07g b .a+6,q s aovqc3b5pu5zh;joopjtates 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 rotat:c /zrkeccl25 ing with constant angular velocity. When the angular velocity is reduced to one-third, the kin2rlcc5k / z:ecetic energy becomes

  12.33: A solid, uniform sphere rolls without slipping on a floor ,m8ug8pn l.q2gy1vis.w/hb balong 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, r750rlxyxe cju4w3p4u,v q7 ozadius r, and 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 soli/ htcdf.;xu) m6lsho,w y+)p rd disk and an ideal uniform ring each have mass M and radius R. Each object begins purely rolling without slipping hlcfw/ 6hd+ xrt. ,y;ps))uomdown a rough inclined plane. The coefficients 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 mass M h7jfh scld,s 6 5k8w66qgiw(ht, wkk1and raw6sh8( j5w67h1kig6, kh, wf dkl cqtsdius R. Each object begins 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 inclinedx2ete92: qmxfms7of , plane. Which one of the following choices best represents the type and directiosxq7,e9mme: 2fx2t f on 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 tt svh7w d/.t3its left end. It is released from an angle θabove the horizontal. What is the magnitude of the angular athd/3 tw.st7v cceleration of the rod about the pivot when the rod is released?

  15.46: A uniform rod oft xx8j ;lhal-hmm *y*hg d-8l9 mass M and length L is fixed to rotate about a frictionless pivot located L/3 from one end. The rod is relea8;h h9jx8m-lx-* *lhgyam t dlsed 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 fixe 9ihbvm.qio/4l;rep/-dh c 3ed to rotate about a frictionless pivot located L/3 from one end. The stick is released from rest incrementally away from bepe;ihcd o/. -mi/ 4 hb3lqvr9eing 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-/pn9.mu n0vw ct( -cw c+ymd*wxi)dd cylinders with equal radii on the entccdwd)nmm0(d xw9-v/c uny p-* +.iwd 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, / *4ncn a7zwsm2 kuq9z vb2qx.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 rot aprv6eij/7fys(9ef-el / y k.ate about an aeea f6jef/ y9l y-/prk7v(i.sxis 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 byh9)a*/rj)7 tocod vmasses M but different radii such t*bd 9/j7r)h yatc o)ovhat $r_x< r_y$. 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 a /qxwpp8o lnikt ;om zg,)86i6horizontalipg 86z6 wn/q )ixpo, 8;olkmt 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 d, 6x*flvc0 e7r njx0*l+ rv y4j6aintrotates clockwise about its centvcx r*66,d+n ntrxla 0l47 iyfje* 0vjer 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 cylinder of mass M=2.00 kg and radius R=10.0 cm is con(f: b/8kyd) lzbcrak3nected about an axis through the center of t/l)zr3cyk(k:8 dafbbhe 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 engine plane are tur+a)ctwg 4nm .q;qa 53gp*j6 r( awmrtsning in a clock wise direction with respect to the pigc3tt.aa gwpaj5;m( *s+r q m 4)6wqrnlot. The 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.