12.43: Several forces act on a rigid body.+pioq8a j s26rg/b j7k If the resultant (net) force on the body is zero, which one of the following statemej8 ji/p brgosqk67 2+ants must be true?

  97.39: A cylinder free to turnaround a fixed axis has a string wrapuqs/zo3yuj+iyhh 87;evnq- 2ped around it as shown to the right. The string is pulled with a force F equz27vuo; 83ns+ujqhh/iy -yq e al to the cylinders weight. What is the acceleration of the string?

  16.16: A uniform stick is fixed to rotate about an axis through7*b k8afhwy.u d4 xeemef)ul3 rh7j9: its center. The stick starts from rest and rotate. :weuk)4 8bd x r fehej7auf9l37*yhms 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 b1 ,ke:skcg/ 6ngres+ K when rotating with constant angular velocity. When the angular velocbe,n /s gke gcsr6k+1:ity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform e*6 c*j1bq+f(7 guey sfsk tt o.5/znvsphere rolls 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 rotfw 2swmk+t 4*i 1e +qhrid1,cwational 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 sjeugvoo ;01(e(/0jwca h9hq solid disk 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 coefficiow;1/je(o haq(j9ue h0vsg0 c ents 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 unro6 wv9y 2n(yxiform ring each have mass M and radius R. Each object begins purely rolling without slixno69(yry2w vpping 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 inclinertht n rsoe (9m 1*(3*xrng6eod plane. Which one of the following choices best represents the type and direction of friction (if any) acting on theox9ens6rr*e h r*3nt1m( t (go cylinder as it rolls up the incline?

  14.43: A long rod of length L is pivoted about iy-uw0d*gw cjrcq1 k0* ts left end. It is released from an angle θabove the horizontal. What is the m-*gqku * r1yc0dc0w jwagnitude of the angular acceleration of the rod about the pivot when the rod is released?

  15.46: A uniform rod5s4nt79x z z6et0y gnn of mass M and length L is fixed to rotate about a frictionless pivot located L/3 from one end. The rod is released from rest incrementally away from being perfectly vertical, resulting in the rod rotating clockwise about the p n40nxsz97 tyt5 g6eznivot. 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 abobgo mx.v.2) lp r:rm;zut 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 center of ma:..bmmlxvporr2) ;z gss about the pivot?

  06.24: A person tries to balance vertically each of three long unifnl5s 1 ewm w(ur(fm:(f+8 e;ezdset 2sorm cylinders with equal radii on the end of hisfms8 zeufdwet:nws1 (2+ml(;5 sere ( 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,l31fib+*xw +f; shi;bmtb(,chc 8ixtqwz 0 w4X 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 eq o 0uew:jih+m0ual mass each are mounted to rotate about an axis fixed through the center of the disk. Each disk is initiallyi0jw+m0oh :eu 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, hav7 b- 6(;mmkjopbf//6d 1s i*yirrkjn te equal masses M but different radii such thajtoidmp/y6 * bkmjr7 (ks6bf n/i-1r;t $r_x< r_y$. 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 hwc3s x/iq0k1 forizontal fo3wsq01xkf/ ci rce 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 5+px h)ygbd9 7 zt9mx shri+v9yix4c* radius R rotates clockwise about its center with ahxd5cp )isit+mb9yzh 9v x47 *yg+x r9n 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=5qb4sytnlzriq-+07 ,3 v/vwq g3t m:eq h5jpr 10.0 cm is connected about an axis th5s 3ybeqwtnr3ti/vm 7l+qhp -vrg4q 05qjz: ,rough the center 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 engine and propeller o.82o xak ;)rkcbkgh:a o vw2p:f 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 direction as the pilot tries to make a kohg 2w:k;xrc pkao :a8vb2) .sharp lefthand turn.