12.43: Several forces act on a rigid body. If the result; 0drgcj 4ms 3rj53e sp9d4qmqant (net) force on the body is zero, which omg 95 3 sd4cdq4rr3m0s;jeqpjne of the following statements must be true?

  97.39: A cylinder free to turnaround)2;4xx 6t:q tbxwwba z a fixed axis has a string wrapped around it as bx:6; twxtax4)2qbwzshown to the right. 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 rotate abouqsn;zl71y;40 gwd dq zt an axis through its center. The stick starts from rest and rotydz;wn4 g7;zd0 lqq1s ates 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 hasnz3;2 0cbpr rdyus*xm,b( ,b m kinetic energy K when rotating with constant angular velocity. When the angular velocity isbs crmnz2,d(bry, b*xu0pm;3 reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slipping on a floor along the uh hkmi 1;g,fg7,jq1b $+x-axis$ (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, a6hqewzm/p31n3 dr m6v dqpi7 :nd 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 u8r9+l9lygf* m9k gyg yniform ring each have mass M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. The coefficients of friction foyy+r*gl9 m9fl9y 8g kgr 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 have masskxfr p/09-m5ezev j 3w M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. The coefficient-ej vxz /pwfkm50e9r3s 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 inclined plaq8cfqe y t x5(9j29jdgs t6m+kb o.l7mne. Which one of the following choices best represents the type and direction of friction (if any) a7mfktl d2. (+ btm59geqjjs96xqyco 8cting 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 from: fkk r,v8n2q ,hjr6h ravvi91 an angle θabove the horizontal. What is the magnitude of the angular acceleration of t 6,,9 f nhriq8rkvjh1rv2a :vkhe rod about the pivot when the rod is released?

  15.46: A uniform rod of mass M and length L is fixed to rotate abouta8 p( *zm z+c)p+ldtiy 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 roypp8cmt*++zz(l )di a tating 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 masn ip wuj.fg;:m(,j9r 5r nfwm7s M and length 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 vertical, resulting .iw9rgumwm r,ffn p:; 5j (jn7in 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 verl, sa,t1tb5m 7sl yr/htically each of three long uniform cylinders w7l, brlth,1/ma 5stsy ith 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 andY, have masse0c 4gx7efh8lws $m_x$<$m_y$, 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 di.) sjy zdcw9u 41fi*edsks of equal mass each are mounted to rotate about an axis fixed through thu*c i.y)j 1sfz94we dde 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, r: w kuav;7f2i6jo;fz X and Y, have equal masses M but different radii such tha:7jzfi2wkfu ;6o; r vat $r_x< r_y$. 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 cyl -g,( bwtp(vkg)dfce,inder with a mass M and radius R is pulled by a horizocdtgg,v),b -k(pw f (ental 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 rad p hp6 ;g6nyrl;u t shuacjxp12/s4w; r0p-u2uius R rotates clockwise about its center with an a p6syp /0u j;uu2xhtw1ah6cr-;u s;nlg2pr p 4ngular 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 16l z3 sap5mhucylinder 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 pulled back, stretching the spring 1.00 ml1 3u5hm za6ps 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 p wye m/p;y11cxropeller 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 ec/1px; m yw1ysharp lefthand turn.