A circular, solid disc of radius R and mass 2M is rotating with angular velocity w. A second disc of radius R and mass M is dropped onto the rotating disc, and the two slide against each other until they reach the same final angular velocity. (a) What is the final angular velocity of the discs? (b) What percentage of the initial KE was lost during the collision?
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- A disk slides toward a motionless stick on a frictionless surface (figure below). The disk strikes and adheres to the stick and they rotate together, pivoting around the nail. Angular momentum is conserved for this inelastic collision because the surface is frictionless and the unbalanced external force at the nail exerts no torque. Before Nail (pivot) (b) Consider a situation where the disk has a mass of 52.4 g and an initial velocity of 33.8 m/s when it strikes the stick that is 1.37 m long and 2.01 kg at a distance of 0.100 m from the nail. After a. What is the angular velocity (in rad/s) of the two after the collision? (Enter the magnitude.) rad/s b. What is the kinetic energy (in J) before and after the collision? K before= p before= kg.m/s K after= c. What is the total linear momentum (in kg. m/s) before and after the collision? (Enter the magnitude.) p after= kg.m/sThree blocks with mass m1=1 kg, m2=2 kg, and m3=3 kg(no angular momentum or energy) are arranged in order on a frictionless horizontal track which is attached to a vertical circular track at the horizontal track's end. The first mass is struck so that it has speed v1. It collides with m2 elastically. Then m2 slides along and collides with m3 inelastically. The final mass enters the circular track of radius of 1 m and reaches an angle pi/3 How much energy is lost during this process?A rod of length 0.50 m and mass 4.0 kg rotates in a horizontal plane about and axis through its center. The rod is at rest when a 3.0 g bullet traveling in the rotational plane is fired into one end of the rod. As viewed from above the bullet's path makes an angle of 60° with the rod. If the bullet lodges in the rod and the angular velocity of the rod is 10 rad/s immediately after the collision, determine the before collision velocity of the bullet. Use conservation of angular momentum. The initial momentum is the point mass momentum of the bullet (the rod is originally at rest). Don't forget to include the bullet when you determine the after collision rotational inertia of the system.
- A disk of mass m₂ = 70.0 g and radius ₁ = 4.50 cm slides on a frictionless sheet of ice with velocity v, where v = 13.00 m/s, as shown in a top-down view in figure (a) below. The edge of this disk just grazes the edge of a second disk in a glancing blow. The second disk has a mass m₂ = 140 g, a radius r₂ = 6.00 cm, and is initially at rest. As the disks make contact, they stick together due to highly adhesive glue on the edge of each, and then rotate after the collision as shown in figure (b). my 11₂ a (a) What is the magnitude of the angular momentum (in kg m²/s) of the two-disk system relative to its center of mass 3.28E-3 x kg m²/s (b) What is the angular speed (in rad/s) about the center of mass? 70.5 X rad/sA large disk of mass Md and radius R is spinning in a horizontal plane about a vertical axis through its center with angular velocity ωi . A person of mass Mp (initially at the center of the disk and for simplicity sake imagine the person is not spinning) walks from the center of the disk to the edge of the disk. Treat the person as a point mass. Find the final angular velocity of the disk.A ring (mass M) and disk (mass M) with radii R rotate in opposite directions.The ring rotates Clockwise with an angular speed 3ω, and the disk rotates Counterclockwise with a speed 2ωThe ring and the disk then "collide" and rotate together with the same ωf. What is the Moment of Inertia of the ring plus disk? What is the Angular velocity, ω of the ring plus disk after the collision?
- A diver (m = 60 kg) jumps from a diving board. At takeoff, his angular momentum about the transverse axis is 30 kg⋅m2/s. His radius of gyration about the transverse axis is 0.5 m at this instant. During the dive, he tucks and reduces his radius of gyrations about the transverse axis to 0.2 m. After he tucks the body, what is his angular velocity about the transverse axis?A point mass m1 = 0.020 kg located at the top corner of a smooth hemispherical bowl m, R. of radius R = 0.450 m is released from rest and hits another point mass m2 = 0.010 kg m2 which is at rest at the bottom of the bowl as shown in the figure. If two masses stick together after the collision, how high above do they go relative to the bottom of the bowl? (Ignore the friction between the %3D masses and the surface of the bowl and take g = 9.8 m/s.)A sanding disk with a rotational inertia of 1.2 x 10-3kgm2 is attached to an electric drill whose motor delivers a torque of 16 Nm. If the torque is applied for 25 ms and the disk starts from rest, what is the magnitude of the angular velocity of the sanding disk? Use the rotational version of the Impulse Momentum Theorem. Take note of the time units.
- As part of a carnival game, a my = 0.653 kg ball is thrown at a stack of 23.8 cm tall, mo = = 0.363 kg objects and hits with a perfectly horizontal velocity of Ubi = 10.8 m/s. Suppose that the ball strikes the topmost object. Immediately after the collision, the ball has a horizontal velocity of bf = 3.10 m/s in the same direction, the topmost object has an angular velocity of @= 1.63 rad/s about its center of mass, and all the remaining objects are undisturbed. Assume that the ball is not rotating and that the effect of the torque due to gravity during the collision is negligible. If the object's center of mass is located r = 16.7 cm below the point where the ball hits, what is the moment of inertia I, of the object about its center of mass? What is the center of mass velocity Uo.cm of the tall object immediately after it is struck? (1) 0 Io = b.J Vo.cm = kg-m² m/sA piece of putty of mass m = 0.75 kg and velocity v = 2.5 m/s moves on a horizontal frictionless surface. It collides with and sticks to a rod of mass M = 2 kg and length L = 0.9 m which pivots about a fixed vertical axis at the opposite end of the rod as shown. What fration of the initial kinetic energy of the putty is lost in this collision? KEJost/KEinitialThe 29-1b rectangular plate is at rest on a smooth horizontal floor. It is given the horizontal impulses as shown in (Figure 1). Assume I = 20 lb. s. Figure 0.5 ft 5 lb.s 60% 2 ft -0.5 ft-- Part A Determine its angular velocity. Express your answer in radians per second to three significant figures. IVE ΑΣΦΑ ↓↑ vec w = 37.747 Submit Previous Answers Request Answer X Incorrect; Try Again; 4 attempts remaining Part B Submit ***** Determine the magnitude of the velocity of the mass center. Express your answer in feet per second to three significant figures. VG = 22.2 ft/s Previous Answers ? rad/s