12.43: Several forces act on a rigid body. xj-pye ryb)1d:9k - --gcxewq If the resultant (net) force on the body is zero, which one of the following statemcpw -ge q1y-x : xb-r)jd9-ykeents must be true?

  97.39: A cylinder free to turnaround a fixed axis has ao8.7 cm) vk( +psumbnz string wrapped around it as shown to the right. The string is pulled with a force F equal to the cylinders weight. What is the acceleration of (vz kb. umcm8po7sn)+ the string?

  16.16: A uniform stick is fixed to rotate about an 0 xe5)lo s5mzn+1mbj1srmjc5 axis through its center. The stick starts from rest and rotates through an angle mjmormesnb5+0 z1cl55)s x1j 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 ri/ g9:facn,ra60m d1zi zu1gkinetic energy K when rotating with constant angular velocity. When the angular velocity is reduced to one-third, the kinetic i mn9 zduc6,gzrif gr:1/1aa0energy becomes

  12.33: A solid, uniform sphere rolls without slipping on a floor along the 4 u)dm+k1cgor5g6xot$+x-axis$ (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 ;jmk*hac:33zgw5kfynh3z+s1 p gw 3lyw9 v. ur, 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 n, av1*)nj-s4yp cx2 ce9f,4ofrpgvseach have mass M and radius R. Each object begi4fye-,p4pc*f,oavcs gnj91vrn )x 2sns 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 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,vnb; sy aedj:s4*hei 25fl4t solid disk and an ideal uniform ring each have mass M and radius R. y5n4 asfvlb2h e4*jd; :,isetEach 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 on a rough i-ikcfrpk 9 q+,nclined plane. Which one of the following choices best represents the type and direction of friction (if any) acting on the cylinder as it rolls up the incline f q-rk+pc,k9i?

  14.43: A long rod of length L is pivoted about its left end. It is rerpyyh +wb(k2 :leased from an angle θabove the horizontal. What is the magnitude of the angular acceleration of the rod about the piv p+r:y2bwh( kyot when the rod is released?

  15.46: A uniform rod of mass M and length L is f1d0ulf3k3fa bpn0g l.r a7s(a ixed 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 magnitude of the tangential acceleration of its center of mass?f 3raufk 7.n1la g3lp0db0 (as

  16.50: A uniform stick of mass M and l, 6im) ke7c0x vb yn;xu s5zmybiu/m+8ength L is fixed to rotate about a frictionless pivot located L/3 from one end. The stick u0 m7i8y yvsm,i +bxku xm5n6ec)z /;b 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 tries to buid3j)jmn9why2( dxi ;1k x)v. f2ipxalance vertically each of three long uniform cylinders with equal radii on the end of his fingerpf.jdxd9 ikw;u 2) (1yvxjh nii 32m)x:
• 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 masse+ f )j-l 4oa/,wljug,tnwud*fs $m_x$<$m_y$, 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 ofvg**s x: anfl3 equal mass each are mounted to rotate about an axis fixed throg: 3fvx*a*nls ugh the 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, X and Y, r 4p.x1y5t lwahave equal masses M but different radii such thx5w4artl .yp1 at $r_x< r_y$. 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 lu6-m8a/ xn8rp2 ecukinder with a mass M and radius R is pulled by a horizontal force 6rxu88 kel2/mnpu-c aF 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 Rm+ 7nf qxq/ rrial1),dm0p i*g rotates clockwise about its center /ldm+i7np)xq*f0i ar,m 1r gq 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 cylinder of mass M=2.00 kg and radius R=10.0 cm is conjoo8 j diq2cz ey7:3(wnected about an axis co8z qjdyo2w( i7e:3 jthrough 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 ang98.d lpptj r5c+rh 5ad 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 in which direction as the pdr5c8a+j .plt h95rg pilot tries to make a sharp lefthand turn.