12.43: Several forces act on a rigihf.,*.nzz g-dsl,i wm d body. If the resultant (net) force on the body is zero, which one of the following hzgdsf .z-*l wnm, ,i.statements must be true?

  97.39: A cylinder free to turnaround a fixed ax.mfa sh*1.bq ri)2aj1ve6kl ris 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 omi1ekalhas.b q *)16 vrj2.frf the string?

  16.16: A uniform stick is fixed to rotate about an axis through 9ys1fhcjp 05uits center. The stick starts from rest and rotates through an angle osc u 51pj0y9fhf $90^{\circ}$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 blo4(e ogp9s6 xrade has kinetic energy K when rotating with constant angulp6soxg9o e4(rar velocity. When the angular velocity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls wi)/yi efa4dmi02+5 ax2eye sov thout 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, radius9/ xna;4 nwsve 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 soliqt, : yknn/u)x9g m/qpd disk and an ideal uniform ring each have mass M and radius R. Each object begins purely rolling without slipping do :9yqmgpk tn)ux//, nqwn 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 ik72wx1muujsu 79 d(l have mass M and radius R. j uxu im197s7dk(uwl2Each 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 inct/sx,m n bsqy9kqqy4dc4fi*9nu0- f5 lined plane. Which one of 9,fs snqibmn* c/k-qqy50t9dyuf 4 4x the following choices best represents 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 8bzeb88 ykkm 7uj; gl ro.f7-vL is pivoted about its left end. It is released from an angle θabove the horizontal. What is the magnitude of th8r kj 8guo8vl 7.7m ;-byfbezke angular acceleration of the rod about the pivot when the rod is released?

  15.46: A uniform rod of mass M and length vgkd-f8r h*b9 L is fixed to rotate about a frictionless pivot located L/3 from one end. The rod is released from rest inh d *b98-gfkvrcrementally 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 nbn bec43fz 7kfw:-f0to rotate about a frictionless pivot located L/3 from one end. The sti7w:n0b fcf nbzkef3-4ck 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 balav+0qrsmm7v5 ad-vy,0 2el uirnce vertically each of three long uniform cylinders with equal raual r i52v7+vv-y0e,rs 0mmdqdii 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 andY, have mas(k ;cwao2g.jhstn 5n 3ses $m_x$<$m_y$, 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 about ai:8u++:y ljdf i1vc+ lhazdd5 n axis fixed through the centerl+8iu:zd +jld if a 1cyd:+v5h 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 masses M but different radii such m4pyhnl v)*hi1s l 0o)thamio 1shh)*lyl0)4v npt $r_x< r_y$. 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 bji s h837dlsa:1c*lsfw 8 luu.y a horizontal force F acufs1cs w*j da8 hl8 l3:is.ul7ting
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 r r o7v40kqv7yqirc 7ka3 z5(vzotates clockwise about its center with an angk7(k73rrc0qy v5qoziv 74z vaular 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 radi- 8lwpgec 6t-lus R=10.0 cm is connected about an axis through the center of the p-wgcl- e l6t8cylinder 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 pifuh142d2q a6ksr c f2ropeller of 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 sharp lefthand turn.246dus21 ffqir ha2ck