12.43: Several forces act onnxam2, :c: fkjl (ypv3 a rigid body. If the resultant (net) force on the body is zero, which one of the following statements must be true yn:kjxm3l ac,(f:pv2 ?

  97.39: A cylinder free to turnaround a fixed axis has (0e ntlln2cd1owu.7 ja string wrapped around it as shown to the right. Thet72cond0n .l l1w(u je 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 anqgsrjt8u t5,i1cr29 bout an axis through its center. The stick starts from rest and rotates throu2 qrgnjct r s1,ti89u5gh 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 kinetb4kq;mejmg:iu *u *m3 ic energy K when rotating with constant angular velocity. When the angular velocity is reduced to one-third, the kinbm*jim:34ge ;ukm qu* etic energy becomes

  12.33: A solid, uniform sphere rolls without slipping on a floor 5suk:r+u zkuysy1.8r 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 sv6qc*u6 h * hm,2+ ktqeuz2qhmass m, radius 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 solid disk and an ideal unifo +dt6(b0 wcozyrm 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 th+ (z bw6cdyo0te 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 a6mo9n+* uj: fkf.hvg, r8wh eM and radius R. Each object begins purely rolling without slipping down a rough inclined plane.e+ho jr6n8g9hf, aw*f: kv.m u 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 i2r.hvdv wcz)- ark8 z1v)j.st nclined 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 the inc kvj vsrad-cr)z2 tv1.zw).h8line?

  14.43: A long rod of length L is pivoted about its left en 4 8, 7qxovuvpa8bjnln8xo4w*i- j+ta d. It is released from an angx* alnv4j+7t,pwu8vqxoi88b an4-j ole 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 and length L is fixed to rotate about a fric) esjqq3qk*5s 5+sv5 r(zqhqm e-4txetionless pivot located L/3 from one end. The rod is released from rest incrementally away from being perfectly vertical, resulting in the rod rotating-evzqm)+eq e5qhr s4 qjks5t3*(sx q 5 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 anm:g xot 7qf.c i7lu1-1bfm;*yphqi i(d length L is fixed to rotate about a frictionless uf; :7t7yxgi 1pm.imf -(1lqc hi obq*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 center of mass about the pivot?

  06.24: A person tries to balance vertically each of th /26j:ytp dtqma5ith+-oej7 5l. vuwyree long uniform cylinders with equal radii on the end of h-io h2/m6t5+wj 5aeu y7.y vpld :ttjqis 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 disksje8c n4 +qxb/b,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 are mounted to rotate a wy22q,vycyx s(h+ d1nbout an axis fixed through the center of the disk. Each disk is initially at rest. The radii of thew+ 2cxvsn1yy ,q2 hd(y 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 tu8fzf:g+is 2z/4t)duhbxsb q((qz7and Y, have equal masses M but different radii such )(fux:tz7q g/q(+f2szs 8 tubibh4dz 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 mass M and radius R is pulled by .,ono0 :inpb0)-e x5;9xjbtaffn g kka horizontal force Fkx,.n0p-5en;gb9:n)iof fao jx b 0kt 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 rotates cgm0o9d,im+b/ voa *zvnw2ec 9lockwise about its center wita2ig/ dm con0b*v9w em9ov,z+h 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 m2kc n vy:q06wbass 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 cylindercb0vny :2 k6wq 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 enxm5j ,sez2w- zgine and propeller of a single engine plane are turning in a clock wise direction with respj,zwz2 em5-sx ect to the pilot. 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.