12.43: Several forces act on:o3. epskylc * a rigid body. If the resultant (net) force on the body is zero, l.c:3eoyp* sk which one of the following statements must be true?

  97.39: A cylinder free to turnaround a fixed axis has a string wrapcb0yhab2ep1c+oet x3g: w( m 6ped around it as shown to the right. The string is pulled6wbat g peyo0b12 ch3:mx( ec+ with a force F equal to the cylinders weight. What is the acceleration of the string?

  16.16: A uniform stik 8warqd:/i+1d2 cv(upb8x5)iasp bkck is fixed to rotate about an axis through its center. The stick starts from r :s(/durdc+a 5i8ak1vxbk 2ibpq)p8w est 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 (ptzj1n za)7 gw :,fwlhyat :7K when rotating with constant angular velocity. When the angular velocity is reduced to one-third, thfjh,7:z() 1pzgw a t7 na:lytwe kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slipping on l n,5c+se 3tdjq+bjfjw93a*ya 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 mx 9uc0f(orjjjsn 9 em/0 r,i9 mek,oq2, 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 u/pkve*9u)ul)ahy cy2 niform ring each have mass M and radius R. Each object begins purely rolling without slipping down a roughu9l2c)*pue hk/ay)yv 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 solid disk and an ideal unifa)j a)kl1b m3 o,wszq:orm ring each have mass M and radius R. Each object begins purely rolling without slipping down a rol,):aq)z aoj3wb1 sk mugh 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 sl vz/m (y1 aw*39hhmqcqipping on a rough inclined plane. Which one of the following choices best represents the type and direction of friction (if any) acting on ty39 / mhqwqz(1a*hmcvhe cylinder as it rolls up the incline?

  14.43: A long rod of length L is pivoted about its left end. It is released fro vxxlr4,x+f9 nw3yvo 1r)mb9bm an angle 9omv xn39, )wbv+lx1 4bxyrrf θabove the 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 of mass M and length L is fixed to rotate about a fufu xghgy3k0.wz3(r)rictionless pivot located L/3 from one end. The rod is released fwu3zfx(g guh 3k.ry 0)rom 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 fixercizx -sk*i/7 d to rotate about a frictionless pivot located L/3 from one end. The stick is re7i zx-is/r k*cleased 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 balance verticanp3fa2v rt3hx.* : unjlly each of three long uniform cylinders with equal r3*2p: u vxrtnf.n3jahadii 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 b r3f/pr:vy( fv 1ocn6masses $m_x$<$m_y$, 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; hysgvl.p/ 3dt an axis fixed through the;h3yl pv.s/dg 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, ha.fw e,bgxj;9y v :;jd )cc*edwve equal masses M but different radii such ,w *y:g9vj dcj bc;) .fex;wedthat $r_x< r_y$. 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 pullebkpc-)a 1r7twjf6k ji4j vtswh 27-f4d by a horizontal forces7fw7 abj) -4421k6vjit tfwj rkc-h p 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, unifor,3chal *j e)blm disk of mass M and radius R rotates clockwise about its cenlla,j*e b)hc 3ter 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 anhek.v0yc v74 dd radius R=10.0 cm is connected about an axis through the cent ye 7c4v.v0hdker 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 single engine plane are t/9:lw50j dg*bco rht furning 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 directioncg 9o j/wbl:f 50h*trd as the pilot tries to make a sharp lefthand turn.