12.43: Several forces act on a rigid body. If the resultant (net) forcm zo,e-pu8:4exj3zrj e on the body is zero, e8, eu4:xzjmj r3-pzowhich one of the following statements must be true?

  97.39: A cylinder free to turnaround a fixed axis has a string wrappeq-knj4 d1 ncn0d around it as shown to the right. The string is pulled with a c 10kq-n4njdn force F equal to the cylinders weight. What is the acceleration of the string?

  16.16: A uniform stick is fixed to rjonw2stjf l(q2h:3 y1 6pxcn9otate about an axis through its center. The stick starts from rest and rotates throu6 qxpf:w 32 jt n1n(clhy29sojgh 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 b.p/thq x(+1,ujnizcqlade has kinetic energy K when rotating with constant angular velocity. When the angular velocity is reduced to one-third, (.t +xihz q1 c/p,qnujthe kinetic energy becomes

  12.33: A solid, uniform spherejyk+1c )s 7bwk rolls without 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 h i2 zrwgusg/ mi5np;:/as mass 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 an ideal uniform ring eaqq jiuknu (jpt/w.57,ch 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 k(w,pu5.qj7i/j t uqnincline 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 -xi hlu57cmim* hq;;r have mass M and radiusm h5lmx-ci*;r iu7;q h 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 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 ohbxjz 14d5 tv8us ::7x8dfqxc n a rough inclined plane. Which one of the following choices best represents the type and direction of friction (ith:v4c5q bxzxd81ds: 8 fj7u xf any) acting on the cylinder as it rolls up the incline?

  14.43: A long rod of length L is pivoted abouj0.nvp:y rjw ;t its left end. It is released from an angle θabove the horizontal. What is the magnitude of the angular acceleration of the rod about the vn; j:y.pr0wjpivot when the rod is released?

  15.46: A uniform rod of mass M and length L is fixed to rotae;iraik i0r) * il0k)gte about a frictionless pivot *ikrai0igr ); ei0)k llocated 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 of the tangential acceleration of its center of mass?

  16.50: A uniform stick of mass M and length L is fixed to rotate about a frictrkm 5vm+9 ( q.kbhmz)wionless 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 pivot. When the 9hv( m+qwkk)b .m5 zrmstick 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 cyli.ci 3qvmdy0(21 kcr p4m+dbccnders with equal radii on the end 0km2ccc3 b(p idrm4qdv1y.c+ 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 dqo;-bd*p 4k i24:kt zdes r6bsisks,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 wuixswt v- t(3uj ;c*-mass each are mounted to rotate about an axis fixed through the center of the;wj u uw( t*t-icx-s3v 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 diffqir 0:l u:f7rlerent radii such :q:lur0 rfl7i that $r_x< r_y$. 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 pul4.cjb54/4cqd qjadvqd .gqu;vc p;08 jp2qp z led by a horizonq .cb52uddg4cv dqcj;v p0 azj8q44/.qqp;j p tal 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, unif-irh*yo g+ d5eehs/, jorm disk of mass M and radius R rotates clockwise about its center with an anguj i5y-e,g+/h *dohrselar 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 cyy e/r cqcb+2k4linder 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 hori cceby +qr/42kzontal 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 propeller of a singewc6hnpvlsurlz5 864 m3l9f o57c+ ekle engine plane are turning in a clock wise direction with respect to the pilot. The gyroscopic7z+6fr4c 63v s5p9h kl 5lm8ceulowne action of the moving parts will cause the plane to move in which direction as the pilot tries to make a sharp lefthand turn.