Consider the rectangular block of mass, M = 2Kg and length L = 2m. Two cylindrical disks(each disk has mass m = 1Kg, radius 0.2 m, velocity of 10 m/s and angular velocity of 250rad/s) simultaneously hit and get embedded into opposite ends of the bar as shown in thefigure. What is the final(a) Linear velocity (Vf) of the system after the collision.(b) Angular velocity (wt) of the system after the collision.HINT: Consider carefully all directions mentioned in the figure.Consider angular momentum about the point "“O". Note the contribution due to both the"spinning" and translation of the disks."spinning" and translation of the disks.V2 = -10m/sv Wz = 250Aud /sM = 2KgVFWi = 250 nad/sMWfV,=10mls9 =0.2m q

a) Let the initial velocity of the rectangular block be vin, and L be the length of the rod. According to the principle of conservation of linear momentum, the initial linear momentum of the system pin before the collision is equal to the final linear momentum pf of the system after the collision. b) The initial angular momentum of the system is calculated in the following way. Note The angular momentum due to the linear motion of the disks is directed normally outwards to the plane of the disks. On the other hand, the angular momentum due to the rotational motion of the disks is directed normally inwards to plane of the disks. Assumption: The angular momentum in the outward direction is positive and the linear momentum in the inward direction is negative. After the collision, the entire system rotates with the same angular velocity. Since the final linear velocity of the system is zero, the angular momentum of the system would be only due to the angular motion. The final moment of inertia of the system would equal to the sum of the moment of inertia of the rod (since we have only the length of the block, so we have considered it to be a rod) about its center of mass, and the moment of inertia of the center of masses of the disks about O. Note that the embedded disks would be treated as the point masses not as the disk. The final angular momentum of the system is calculated in the following way. According to the principle of conservation of angular momentum of the system,

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Consider the rectangular block of mass, M = 2Kg and length L = 2m. Two cylindrical disks (each disk has mass m = 1Kg, radius 0.2 m, velocity of 10 m/s and angular velocity of 250 rad/s) simultaneously hit and get embedded into opposite ends of the bar as shown in the figure. What is the final (a) Linear velocity (Vf) of the system after the collision. (b) Angular velocity (wr) of the system after the collision. HINT: Consider carefully all directions mentioned in the figure. Consider angular momentum about the point "O". Note the contribution due to both the "spinning" and translation of the disks. “spinning" and translation of the disks. V2 = -10m/s Wz =250 nad |s VE M = 2Kg WI =250 nad/s MWf 4 m V, =10mls 1=0.2m ↑

Consider the rectangular block of mass, M = 2Kg and length L = 2m. Two cylindrical disks (each disk has mass m = 1Kg, radius 0.2 m, velocity of 10 m/s and angular velocity of 250 rad/s) simultaneously hit and get embedded into opposite ends of the bar as shown in the figure. What is the final (a) Linear velocity (Vf) of the system after the collision. (b) Angular velocity (wr) of the system after the collision. HINT: Consider carefully all directions mentioned in the figure. Consider angular momentum about the point "O". Note the contribution due to both the "spinning" and translation of the disks. “spinning" and translation of the disks. V2 = -10m/s Wz =250 nad |s VE M = 2Kg WI =250 nad/s MWf 4 m V, =10mls 1=0.2m ↑

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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