12.43: Several forces act on a rigid body. If the resultant (net) force on thee uj6f*w rm8uyvpc54gna7 n+*s nk+d* body is zero, which one of e8ra 4k gunm5d nj*vny cf +**wups76+the following statements must be true?

  97.39: A cylinder free to turnaround a fixed axis has a string wrapped ar)9+lbnnb( qce hky8 6vound it as shown to the right. The string is pulled with a force F equal to the cylinders wein l b8)vyb(9qnkhe6+c ght. What is the acceleration of the string?

  16.16: A uniform stick is fixed to rotate about an axis through its cenpdyk7b-y b1f 1ter. The 7pbyfb1k1 y d-stick starts from rest and rotates 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 r,hl/agt dhornu *; lxv i8):1.ah+(hss * kcjiotating with constant angular velocity. s v1 naixh i:*a h+g)t/*j8 rldc.(su;ohhk,l When the angular velocity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slipping on a floor along 16d2jv0 izm:/1hd1ts z/aetfca1i n nthe $+x-axis$ (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 rotationax+(o (s+cgdal l 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 unif p:+j9;(owsm/x /n cp nyz*lntorm ring each have mass M and radius R. Each objy/ 9;+ntwjn /:oc* zs( pnplmxect 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 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 idea ;p35ysakm qyify.09q l 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 with the incline 5am iyqq0 p9y.syf;3kare $μ_disk> μ_ring$.
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 slippia:pg*b* ;)0/j5:lt a tblvhlxpaena ,ng on a rough inclined plane. Which one of the following choices best represen h: ;/t :gpaa*l)tae5b panbjxl0*vl,ts 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 L is pivoted about its left end. It is released frpfs( hiq k8v q29rp;,yom an angle θabove the8s,prphv i fqq ;(2yk9 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 wvndi7mt e3 80about 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 pivot. When the rod is horizontal, what is the magnitude of3nvid807tw me the tangential acceleration of its center of mass?

  16.50: A uniform stick of mass M and length L is fixed toggz yj45n3jhu2u)8j,cjbv 73 k wbbn5 rotate about 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 pivokv7 45h83u j,n3ybcjn2 bjug) gwj5bzt. 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 vertic 77vmd-rla6axinrh (5ally each of three long uniform cylinders with equal radii on the end of his fing57r (7rhx l6i-m davaner:
• 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 maske+vjxp1( l8n-p 5ltyses $m_x$<$m_y$, 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 e55 y9 av;ewiaj4jy19 :foc:lois 6yi qach are mounted to rotate about an axis fixed throughfiq19 wl coi;yav:j9a 5i:jy4eo6sy5 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,yf1qoi82i 8q.. igfwncik7 .k have equal masses M but different radii such tf8 q .7 iik.oigi k.fwn2q8cy1hat $r_x< r_y$. 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 ragm) .vx4t ulj)dius R is pulled by a horizo v x4)gjt)lu.mntal 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 * kl8u1k:f r hlkn3-(ghdqx;yrotates clockwise about its cente k1hq*grllkn d(uk;:3yhx 8f-r 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 Rca9r5:smd k )bhd166vag/yz b=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 cylinder is pulled back, stretching the spring 1.00 m from equilibrium. When released, the cylinder rolls61 v b dzhg6km/c9aya)5:dbrs without slipping. What is the speed of the center of the cylinder when it returns to equilibrium?

  01.39: Suppose the engi j8yf930 v7sgbid/jm1y 0otqrne and propeller 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 pilosir7180ft 3ymy/ jdojbqv0g9 t tries to make a sharp lefthand turn.