A cockroach of mass m lies on the rim of a uniform disk of mass 5.00m that can rotate freely about its center like a merry-go-round. Initially the cockroach and disk rotate together with an angular velocity of 0.300 rad/s. Then the cockroach walks half way to the center of the disk. (a) What then is the angular velocity of the cockroach-disk system? rad/s (b) What is the ratio K/Ko of the new kinetic energy of the system to its initial kinetic energy? (c) What accounts for the change in the kinetic energy? (Select all that apply.) O centrifugal force O friction O cockroach does negative work on the disc O centripetal force O gravity O cockroach does positive work on the disc
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- A uniform thin rod of length 0.48 m and mass 3.5 kg can rotate in a horizontal plane about a vertical axis through its center. The rod is at rest when a 3.2 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 9.00 rad/s immediately after the collision, what is the bullet's speed just before impact? Axis Number i UnitsA 97.9 kg97.9 kg horizontal circular platform rotates freely with no friction about its center at an initial angular velocity of 1.55 rad/s1.55 rad/s. A monkey drops a 9.51 kg9.51 kg bunch of bananas vertically onto the platform. They hit the platform at 4545 of its radius from the center, adhere to it there, and continue to rotate with it. Then the monkey, with a mass of 20.5 kg20.5 kg, drops vertically to the edge of the platform, grasps it, and continues to rotate with the platform. Find the angular velocity of the platform with its load. Model the platform as a disk of radius 1.73 m1.73 m.A disk-shaped merry-go-round of radius 2.53 mm and mass 135 kg rotates freely with an angular speed of 0.641 rev/s . A 65.4 kg person running tangential to the rim of the merry-go-round at 3.51 m/sm/s jumps onto its rim and holds on. Before jumping on the merry-go-round, the person was moving in the same direction as the merry-go-round's rim. What is the final angular speed of the merry-go-round?
- A playground merry-go-round with a mass of 145 kg and a radius of 1.9 m is rotating with an angular frequency of 0.42 rev/s. -What is the magnitude of its angular velocity, in radians per second, after a 17 kg child gets onto it by grabbing its outer edge? The child is initially at rest.Angular momentum is conserved for this inelastic collision because the surface is frictionless and the unbalanced external force at the nail exerts no torque. The disk has a mass of 51.5 g and an initial velocity of 32.0 m/s when it strikes the stick that is 1.40 m long and 2.05 kg at a distance of 0.100 m from the nail. 1. What is the angular velocity (in rad/s) of the two after the collision? (magnitude in rad/s) 2. What is the kinetic energy (in J) before and after the collision? Kbefore= J Kafter= J 3. What is the total linear momentum (in kg · m/s) before and after the collision? (Entermagnitude) pbefore= kg · m/s pafter= kg · m/sTwo blocks are released from rest on either side of a frictionless half-pipe (see the Figure below). Block B is less massive than block A. The height HB from which block B is released is less than HA, the height from which block A is released. The blocks collide elastically on the flat section. HA B HB 1) After the collision, which is correct? Block A rises to a height greater than HA and block B rises to a height less than HB. Block A rises to a height less than HA and block B rises to a height greater than HB. Block A rises to height HA and block B rises to height HB. Block A rises to height HB and block B rises to height HA. The heights to which the blocks rise depends on where along the flat section they collide. Submit
- A uniform disk of mass 7 kg and radius 0.2 m is free to rotated about an axis perpendicular to its center. A constant force of size 146 N acts at the edge of the disk, in a direction tangent to that edge. The force acts until the disk has completed 169 full rotations. What is the angular momentum of the disk after those rotations are complete, in kg m2/s? It could be useful to you to know that the rotational inertia of a uniform disk is 1/2 M R2. (Please answer to the fourth decimal place - i.e 14.3225)A crustacean (Hemisquilla ensigera) rotates its anterior limb to strike a mollusk, intending to break it open. The limb reaches an angular velocity of 175 rad/s in 1.50 ms. We can approximate the limb as a thin rod rotating about an axis perpendicular to one end (the joint where the limb attaches to the crustacean). If the mass of the limb is 28.0 g, the length is 3.80 cm, and the extensor muscle is 3.00 mm from the joint and acts perpendicular to the limb, what is the muscular force required to achieve the blow?In the figure, a 6.04 g bullet is fired into a 0.604 kg block attached to the end of a 0.904 m nonuniform rod of mass 0.435 kg. The block- rod-bullet system then rotates in the plane of the figure, about a fixed axis at A. The rotational inertia of the rod alone about A is 0.0372 kg-m2. Treat the block as a particle. (a) What then is the rotational inertia of the block-rod-bullet system about point A? (b) If the angular speed of the system about A just after impact is 5.03 rad/s, what is the bullet's speed just before impact? Rod Block Bullet
- Three objects lie in the x, y plane. Each rotates about the z axis with an angular speed of 7.48 rad/s. The mass m of each object and its perpendicular distance r from the z axis are as follows: (1) m1 = 7.80 kg and r1 = 5.20 m, (2) m2 = 3.10 kg and r2 = 2.90 m, (3) m3 = 3.50 kg and r3 = 4.70 m. Find the tangential speed of (a) object 1, (b) object 2, and (c) object 3. (d) Determine the total kinetic energy of this system using the expression (e) Find the rotational kinetic energy of the system using the relation to verify that the answer is the same as that in (d).The figure shows a device that can be used to measure the speed of a bullet. The device consists of two rotating disks, separated by a distance of d = 0.922 m, and rotating with an angular speed of 90.8 rad/s. The bullet first passes through the left disk and then through the right disk. It is found that the angular displacement between the two bullet holes is = 0.360 rad. From these data, determine the speed of the bullet. Number i Bullet Units 19 kd + MotorA uniform thin rod of length 0.78 m and mass 3.3 kg can rotate in a horizontal plane about a vertical axis through its center. The rod is at rest when a 3.3 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 12.0 rad/s immediately after the collision, what is the bullet's speed just before impact? Number i Units Axis