The figure is an overhead view of a thin uniform rod of length 0.486 m and mass M rotating horizontally at angular speed 20.0 rad/s about an axis through its center. A particle of mass M/3 initially attached to one end is ejected from the rod and travels along a path that is perpendicular to the rod at the instant of ejection. If the particle's speed v, is 7.96 m/s greater than the speed of the rod end just after ejection, what is the value of v,? Rotation axis Number i Units eTextbook and Media Save for Later Attempts: 0 of 8 used Submit Answer
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- A uniform rod of mass 210 g and length 100 cm is free to rotate in a horizontal plane around a fixed vertical axis through its center, perpendicular to its length. Two small beads, each of mass 22 g, are mounted in grooves along the rod. Initially, the two beads are held by catches on opposite sides of the rad's center, 12 cm from the axis of rotation. With the beads in this position, the rod is rotating with an angular velocity of 16.0 rad/s. When the catches are released, the beads slide outward along the rod. (a) What is the rod's angular velocity (in rad/s) when the beads reach the ends of the rod? (Indicate the direction with the sign of your answer.) rad/s (b) What is the rod's angular velocity (in rad/s) if the beads fly off the rod in a tangential, straight line path? (Indicate the direction with the sign of your answer.) rad/sTwo 3.40 kg balls are attached to the ends of a thin rod of length 44.0 cm and negligible mass. The rod is free to rotate in a vertical plane without friction about a horizontal axis through its center. With the rod initially horizontal (the figure), a 73.0 g wad of wet putty drops onto one of the balls, hitting it with a speed of 2.97 m/s and then sticking to it. (a) What is the angular speed of the system just after the putty wad hits? (b) What is the ratio of the kinetic energy of the system after the collision to that of the putty wad just before? (c) Through what angle (deg) will the system rotate before it momentarily stops? Putty wad Rotation axis (a) Number i Units (b) Number i Units Units i (c) NumberTwo 3.50 kg balls are attached to the ends of a thin rod of length 36.0 cm and negligible mass. The rod is free to rotate in a vertical plane without friction about a horizontal axis through its center. With the rod initially horizontal (the figure), a 42.0 g wad of wet putty drops onto one of the balls, hitting it with a speed of 3.25 m/s and then sticking to it. (a) What is the angular speed of the system just after the putty wad hits? (b) What is the ratio of the kinetic energy of the system after the collision to that of the putty wad just before? (c) Through what angle (deg) will the system rotate before it momentarily stops? Putty wad Rotation axis
- A projectile of mass .050 kg moves to the right with a speed of 4.0 m/s. The projectile strikes and sticks to the end of a rod of mass 0.8 kg, at length 1.2 m from the rod's centre. The rod may rotate freely around a stationary axle pinned through the rod's centre of mass. Find the magnitude of the angular velocity, ω, of the system right after the collision.The figure shows an overhead view of a 2.70 kg plastic rod of length 1.20 m on a table. One end of the rod is attached to the table, and the rod is free to pivot about this point without friction. A disk of mass 53.0 g slides toward the opposite end of the rod with an initial velocity of 20.5 m/s. The disk strikes the rod and sticks to it. After the collision, the rod rotates about the pivot point. (a) What is the angular velocity, in rad/s, of the two after the collision? rad/s (b) What is the kinetic energy, in joules, before and after the collision? KEi = J KEf = JConsider a spacecraft orbiting Earth. At an instant in time, the angular velocity of the spacecraft relative to Earth is = 1.9bh +0.82b2+0.34b3 (in rad/s) and the angular acceleration of the spacecraft relative to Earth is a = 0.0561 +0.19bz+0.22bg (in rad/s?). What is the moment (in N.m) being applied on the spacecraft in the b2. Assume the moment of inertia of the spacecraft is given by: Г5000 0.0 0.0 0.0 10000 0.0 kg.m? 0.0 13000 Note b1, b2, bz are unit vectors fixed in the spacecraft reference frame.
- Two 4.80 kg balls are attached to the ends of a thin rod of length 40.0 cm and negligible mass. The rod is free to rotate in a vertical plane without friction about a horizontal axis through its center. With the rod initially horizontal (the figure), a 690 g wad of wet putty drops onto one of the balls, hitting it with a speed of 4.21 m/s and then sticking to it. (a) What is the angular speed of the system just after the putty wad hits? (b) What is the ratio of the kinetic energy of the system after the collision to that of the putty wad just before? (c) Through what angle (deg) will the system rotate before it momentarily stops? Putry wad Rotation axis (a) Number Units (b) Number Units (c) Number UnitsA uniform disk of mass M is rotating freely about its center. On its rim lie a cockroach of mass M/9. Initially the cockroach and disk rotate together with an angular velocity of 3.2 rad/s. Then the cockroach walks halfway to the center of the disk. What is the new angular velocity of the system?The figure shows a small piece of clay colliding into a disk. The disk is initially at rest, but can rotate about a pivot fixed at its center. The collision is completely inelastic.1) The disk has mass M = 4.73 kilograms and radius R = 0.755 meters. The clay has mass m = 279 grams and is moving horizontally at vi = 3.66 m/s just before colliding with and sticking to the disk. The clay strikes the edge of the disk at a location of b = 0.505 meters offset from the center of the disk. Note that the size of the clay is negligible compared to the radius of the disk. 2) Calculate the angular velocity (rad/s) of the disk just after the collision.
- A rod of mass M = 3.25 kg and length L can rotate about a hinge at its left end and is initially at rest. A putty ball of mass m = 65 g, moving with speed v = 5.63 m/s, strikes the rod at angle θ = 55° from the normal at a distance D = 2/3 L, where L = 1.25 m, from the point of rotation and sticks to the rod after the collision. a) What is the initial angular momentum of the ball, in kilogram meters squared per second, right before the collision relative to the pivot point of the rod? b)What is the total moment of inertia If with respect to the hinge, of the rod-ball-system after the collision, in terms of the variables from the problem statement? c) What is the angular speed ωf of the system immediately after the collision, in radians per second?A uniform thin rod of length 0.73 m and mass 3.0 kg can rotate in a horizontal plane about a vertical axis through its center. The rod is at rest when a 4.4 g bullet traveling in the rotation plane is fired into one end of the rod. As viewed from above, the bullet's path makes angle 0 = 60° with the rod. If the bullet lodges in the rod and the angular velocity of the rod is 11.0 rad/s immediately after the collision, what is the bullet's speed just before impact? Ахis Number Units