12.43: Several forces act on a rigid body. If the resultant (net) force on thk6n1:v;bp,q zswt5 cce body is zero, which one 15 c:;cqnzbwkp,s6vtof the following statements must be true?

  97.39: A cylinder free to turnaround a fixed axis has a string wrw 3v.pt6(fcb tapped around it as shown to the right. The string is pulled with a force F equal to the cylinders weight. c3tf vt.pb( w6What is the acceleration of the string?

  16.16: A uniform stick is fixed to rotate about anppw;c38k c quwm:gy7/ axis through its center. The stick stqmp wku:;/3pg7 cy8cwarts 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 has9zt toc)),xjlg8 l ag+ kinetic energy K when rotating with constant angular velocity. When the angular velocity is reduced to one-third, the kinetic energy become9z)l x t,gg ao+l8ctj)s

  12.33: A solid, uniform sphere rolls without slipping on a floor j jn7ab, 9i+fmalong 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, radinjdu819oob z8 3zskeudb 3m6x 5go(8uus 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 solid6t r :wfjpz:+q*1s).pw onqy sv(8gmjvyi. q6 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 frqj+szq6 jp m1trq s(vg y:6.yp.)o8n*f:ww i viction 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 woths+8b 7+a hb*ab0 ftxi3 9nand 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 with the incline+7sxo+tawfth bnba08 b3* hi9 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 a5/ldd q;:j;h re d: ixizm.yk* rough inclined plane. Which one of the following choices best represeq;d jd:ki.ey /5*;l:r imzdxh nts 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 pivo ko31*y21q6 c btx3r;wbicn eo)b*e smted about its left end. It is released from an angle θabove the horizontal. What is the magnitude of the angular accexn bce6ceo* y) qb;3ir3 1t*wbs m21koleration of the rod about the pivot when the rod is released?

  15.46: A uniform rod of mass M and length L is fi ;.zov6 ah +mabxgb:ox9wv(+jxed to rotate about a frictionless pivot located L/3 from one end. The rod is released from rest incrementally away from being perfectly vertical, resubhx . a6++vv(xo9zbm;:owa jg lting 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 lengthwk/rb -ttetc+:vn l 6p4qj.8 m L is fixed to rotate about a frictionless pivot located L/3 from one end. The stick is released from rest incrementally away from being perfectly.q+mtt /wcjrn6 ek:4tb -8plv 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 three long uniform cylinders/5ep2 ygdwx9ezt)b -q x ep2e59 -wyb)zgqt/dwith 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 disk5(sxal1 3 pzmrs,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 7d + tccbhnwas:h- 3p)ku42m lx7ik0urotate about an axis fixed through the center of the disk. Eac muhwc7 xip)scbtn47+u20:h3 lak- kdh 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 y3 y2s5e xljbkggf k 9q36h*+pthk fp2 k+hxy 3 qs396*5ggljebyat $r_x< r_y$. 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 pulledf2q+ww9e g(e ill-+sb)ee v:n by a horizontal fl e+:ese(l)-2bw+ien gq9v fworce 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 rotates clockwise x, gzf 2fr(;xsabout its ce,;rg x fxfz2(snter 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 cylindem -u eo0(;*hl5ua(rry7w zkfqr of mass 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 cylinder is pulleyaozk;u r7 eu*( w- fqrh05(mld 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 single engine,shtb:pf k93 c plane are turning in hck,:3f ptb9 sa 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.