12.43: Several forces act on a rigid body. If the resultant ag(bif7 ,li+n(net) force on the body gi,+7l nfai(bis zero, which one of the following statements must be true?

  97.39: A cylinder free to turnaround a fixed axis hatr+mwajc yp: -v7/ld4s a string wrapped around it as shown to the right. The string is pulled with a force F equal to the cylinders weight. What isca-t:d7+vry4wl jp /m the acceleration of the string?

  16.16: A uniform stick is fixed to rotate about an axis through its centpxqz30 * ap(nder. The stick starts from rest and rotates th* zp(nx3pq0a drough 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 rotating with consta68e/:yg5 tqfocm +j3chrn9w wnt angular velocity. When the angular velocity is re +8y9:q36wf/woe r5gmct hcj nduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slny/g0c 8 z wp4bm8pv,zipping 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 m f52(kc p:ulvqass m, radius 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 solid disk and 1fd i )wmb5r0q- uy8ucan 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 disk05umrwiucbfy d1q-8 ) 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 have mass h7jw3 fsoac 07ufs9*hM and radius R. Each object begins purely rolling without slipping down a rough iojf770sa cswh* 9huf 3nclined 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 p7v1f-3pq6stbsi ;iqqdd 7 ,(k abcf-a rough inclined plane. Which one of the following choices best represents the type and dv aq,(; -f d3pi1 7dbp-iqsqtkcb67fsirection 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 left9dcwou mx4r *m;q zm1. end. It is released from an angle θabove theqdrczu 1omm*;4 9.xmw 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 5k4 tqe3 pa+kkof 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 pivot. When the rod is horizontal, what is the m35kkk+at 4 eqpagnitude of the tangential acceleration of its center of mass?

  16.50: A uniform stick of mass M and len :+qv a-8cm9*dtlgv xsgth L is fixed to rotate about a frictionless pivot located +d x*9g8mv lcq svt-a: 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?

  06.24: A person trieiln:d1y(.5 nf9bn2lp xu r(xwl+ /gkws to balance vertically each of three long uniform cylinders with equal rad xn.lif(/ywl5nr(+g1kw2nl :x pbd9u ii 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, hx1-gxfd *37wm2 nknzl rsv n2.ave 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 ar( v d82qz mx:w;snt6nre mounted to rotate about an axis fixed through the center of the disk. Each disk is initially at rest. The radii of the diskrtv8s;xnw:(nz2 q dm 6s 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 rveo9+t *ec; w 5voomtd l0x6p3a6h-ieadii such that oeox*9hc v0l v 6tiepe+ t;wo356adm-$r_x< r_y$. 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 vc1 9zx4)6- vs:jl97 b;bzba,etpdsvvfbl8q by a horizontal force vla-1 z4)c b79 vlf86 p9,t ve:jvbdsz;qbxbsF 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 ahlb+*2.n/ opvbc i8jmbout its center with an angulablpoh8*c. +iv nb/2 jmr 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=2wvm3r.iumafo m.h n* 6j9ta01 ibnn -(.00 kg and radius R=10.0 cm is connected about an axis through the centun-n9*wo(16thr vabnf0ia. m. 3mmjier 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 en9.1cr kv*nq d ,jqc+z0-zlsm)a8vp ebgine 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 l,p9c +bqmdvc-1vsj *zaq ke0nr).8zin which direction as the pilot tries to make a sharp lefthand turn.