12.43: Several forces act4ihwrly90 a23hz 6asbw o+ .cr on a rigid body. If the resultant (net) force on the body is zero, which one of the following statementz6 2o.ilwh4s 3 brr0+acwyah9s must be true?

  97.39: A cylinder free to turnaround, 6zngxpx 9z+w a fixed axis has a string wrapped around it as shown to the right. The string is pulled with a force F equal to the cylinders w6+,zwxz gpx n9eight. What is the acceleration of the string?

  16.16: A uniform stick is fixed to rotate about an axis through its cenu qr3sdebtpu+7; scqf 8)9v .nter. The stick starts from res9q7s tfvdbuqp n)3 sc.ur; +8et 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 rotating with bw c d-dy-+v:bl4)ebrconstant angular vel bcebyvr-d +:4b-)dw locity. When the angular velocity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls , g q4jmqd7d. 6+q3h*8xj+zg lreyivn 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 has mass m, radius r, zv+n;3x-2; dfso zy46nogzcw e 6a 2bcand 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 r4yf5ew 451 ghk: gki9og b2oyjing each have mass M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. The co kyj9ewokgyifo: h412 5gb4 5gefficients 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 disz6 ho*uidzt 9 kqvill39:y qh*i39*qpk 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 friction for theqv yipd9o6l9 zi lt i 9hquh**k:q3z*3 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 o, 9sef;bez -+u pg6sypqo6m/ en a rough inclined plane. Which one of the following choices best represene 9/-geys 6zspqbopu ef6, ;+mts 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*rz 3zrk*xp:j f8zv fyv6l+ w/ is pivoted about 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 pivot when the rod is :xv y+ kp*v8fw6fjr/3lzrz*z released?

  15.46: A uniform rod of ma z 1io8n/y pyj ;c8cxqo+3adz8ss 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 rodpca 3j/88oc8nzqx 1i+zd;yy o 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 k ;u q./ke5rgwa 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 pivot. 5 /. quwr;ekkgWhen 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 longa q9q hc8 +txhk:;i.ay uniform cylinders 8q hhay.:+;xqca9 tikwith 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 andr stw +lj:j2:x nrga5/Y, 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 rotate abou 4lferu-84itrc9wy p:t an axis fixed through the center of the disk. Each disk is initially at rest. Ttil 8rfcry4: 94pw u-ehe 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 difaig4mwvhm sfg2l -82c18+w cevfzex w /(l;y8ferent radii such that lmlw hxz- /8+v2e 48 w8(; ffv gegcs1ami2wcy$r_x< r_y$. 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 mass5rps9 eg4b6hwx 5f( lc M and radius R is pulled by a horizontal fo49cr s5e h (xwp5bglf6rce 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 andjfbf6e/fg7 59s/k5+vi rbailz 4yn .u radius R rotates clockwise about its center with an g 5i4vai6n9 ff7jf / su./kb5lre+bz yangular 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 radlcbso 5:drl/ hz(n3i, ius R=10.0 cm is connected about an axor/s,n bli(3dch5:zl is 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 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 singl8y)ihliaj 6wa; z85nme engine plane are turning in a clock wise direction with respect to the pilot. The gyroscopic action of the moving parts whwl8i5y6j;i am) za n8ill cause the plane to move in which direction as the pilot tries to make a sharp lefthand turn.