12.43: Several forces act on a rigid body. If the resultant o 3g bc8njzqa1.gar;: (net) force on the body is z;anbg q18a: gj3.czr oero, which one of the following statements must be true?

  97.39: A cylinder free to tup*abzecx*qr+3+ i cx1rnaround a fixed axis has a string wrapped around it as shown to the righteq ba+c*+z3p1*xxc i r. 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 rosjosba+ q(2m)(jw y/d tate about an axis through its center. The stick starts from rest and rotates)2 qdj+mjs/(w(soay b 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 energyyfj + cp e4pyscv 2hza3:;)a1y K when rotating with constant angular velocity. When ty cep3j4;fha2y s+ 1py:)zv ache angular velocity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slipping on a f 1ntdb9cwou//. yo-lploor 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, andz1mpyd7tkv y.74 op e/ 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 unif4ey wyv ubw. (ht5 ubtp6;vs25orm 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 and ring with the incline2 yue5wtbsv vwt4yh ;(.6pb 5u 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 unifou (t5 :q)9 ufqbalaay3rm 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 coefficients of friction for the disk and ring )uy 3lqa:9( t fubaq5awith 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 slippiq9co))*f /)k. sug lyzy,mx 7*mnrzzang on a rough inclined plane. Which one of the following choices best represents the type and direction of friction (if any) acting on the cylinderz zc u/m)*zs*qx 7y)ay,lm )gfo9krn . as it rolls up the incline?

  14.43: A long rod of length L is pivoted about its left end. so7w-5bpzl 3vor;j v) It is released from an angle θabove the horizontal. What is the magnitude of the angular acceleration of the rod about the pivob)jw3o;7v rv l5spo-zt when the rod is released?

  15.46: A uniform rod of mass M and length L is fixedl8e8p orcq jw*:.g6 qy 65jvqb,d 1zpd to rotate about a frictionless pivot located L/3 from one end.qc5,b68 wj z qyv*gd 1rl popqjed68.: 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 to rotate a,8kiwla6/nkd,yk3tj i s f *0ebout 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 mass about the pivot?3 ail s 0kifdk*yn,,e 8k/6tjw

  06.24: A person tries to balance vertically each of three long uniform j ar8/eyvxfv :(4 tqxcd 14o8u)9anbdcylinderstqajvx ad8enf9 x8 ud1vb:4) (rcy/o4 with equal radii on 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 at.yo+7khyy /z ndY, 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 moujckw.f +. :uyc01p1 fcqe)bttnted to rotate about an axis fixed through the center of the disk. Each disk is initially at rest. The radii of the disks apf+. 1twec: b 1cu. j0q)ytkcfre $r_1 < r_2$. 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 equal9ffb q6 5viz4e masses M but different radii such thz96 fif 45bvqeat $r_x< r_y$. 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 cylindhw m41fb7t x2zzlol7*er with a mass M and radius R is pulled by a horizontalxzlt*w74zhbf7mo12 l 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 yp) ; -dz8otxki;c4,4fykl )wgxbo 1krotates clockwise about its center with an anguit)-o ;w )of k4;8xl,dk1y 4ygcxbzp klar 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 4k.c azk me4,zigzid5hq+2e)kg and radius R=10.0 cm is connected about an axis through the center of thek+dhg me.ek zz4az4) 2q,iic5 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 y, sseb7t2zt hztb0 9 p0bu89asingle 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 pi 0ps0tt ts8 ea97bbb ,2yhz9uzlot tries to make a sharp lefthand turn.