5. Fig. 3 shows the overhead view of a uniform thin rod of length I and mass M that can rotate freely about a fixed axis on a horizontal surface. The rod is at rest initially with moment of inertia MI?. A bullet of mass m is fired towards one end of the rod with initial velocity v. After piercing the rod, the bullet's velocity is reduced to v. The angular velocity of the rod after being shot through is ( ) 3mv A. ZMI 7mv В. 4MI overhead view mv C. MI Fig 3 D. Smv 3MI

5. Fig. 3 shows the overhead view of a uniform thin rod of length I and mass M that can rotate freely about a fixed axis on a horizontal surface. The rod is at rest initially with moment of inertia MI?. A bullet of mass m is fired towards one end of the rod with initial velocity v. After piercing the rod, the bullet's velocity is reduced to v. The angular velocity of the rod after being shot through is ( ) 3mv A. ZMI 7mv В. 4MI overhead view mv C. MI Fig 3 D. Smv 3MI

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Similar questions

In the helicopter shown; a vertical tail propeller is used to pre- vent rotation of the cab as the speed of the main blades is changed. Assuming that the tail propeller is not operating determine the final angular velocity of the cab after the speed of the main blades has been changed from I80 to 240 rpm. (The speed of the main blades is measured relative to the cab, and the cab has a centroidal moment of inertia of 650 lb.ft.s2. Each of the four main blades is assumed to be a slender rod 14 ft weighing 55 lb.)
A disk with mass m and radius R is released from rest at a height h and rolls without slipping down a ramp. What is the velocity of the center of the disk when it reaches the bottom of the slope? (Hint Use the work-energy principle. At each instant the disk rotates around the contact point C, thus the inertia used for rotatonal kinetic energy should be computed around point C not point G.) m C h
Two disks A and B, of mass m 1 kg each and of radius 10 cm, are placed on a horizontal table. The disk A is launched in translation with a speed of 10 m/s along the y axis, B is at rest. The coefficient of kinetic friction between the disks is 0.5. The line of impact is at an angle of 60° with the x-axis. The moment of inertia of each disk around its center of mass is I = 1₂ = 0.005 kg.m². The coefficient of restitution between the two disks is e=0.6. a) Determine the velocities of the centers of the two disks, just after the impact. b) Calculate the angular velocities of the disks, just after the impact. c) Calculate the energy loss during the impact.
A massive sphere, with 10,0cm radius and moment of inertia I=4,00 x 10-3 kg-m² in relation to a straight line passing through the center of mass, rolls without sliding, descending a surface with an inclination of 30º in relation to the horizontal. In a certain initial position the total kinetic energy of the sphere is 17.5j . a Sketch the physical situation by identifying all the forces acting on the sphere in the initial position. (b) How much of this initial kinetic energy is due to rotation? (c)
Model the arm ABC as a single rigid body. Its mass is 320 kg, and the moment of inertia about its center of mass is | = 390 kg-m². Starting from rest with its center of mass 1.4 m above the ground (position 1), the ABC is pushed upward by the hydraulic cylinders. When it is in the position shown (position 2), the arm has a counterclockwise angular velocity of 1.0 rad/s. How much work do the hydraulic cylinders do on the arm in moving it from position 1 to position 2? Th -1.80 m -1.40 m- B 0.30 m 0.80 m 0.70 m 2.25 m C
A large bug of mass m crawls directly outward from the center of a disk with moment of inertia I and radius R that is free to rotate on a frictionless axle about its center. The disk spins at an initial angular velocity wo when the bug is at the center of the disk. If the bug takes a path defined by r(t) = R, where t; is the known time it takes for the bug to reach the edge, what will be the angular velocity of the system as a function of time (consider only times t < t;)? Law Application
2 An object is made of two identical uniform 3m long rods connected as shown. The total mass of the system is 60kg. The object can rotate in the plane of the page about a fixed axis at Point A. There is a friction moment of 500 N m about point A. a. What is the mass moment of inertia of the object about Point A? b. If the object is released from rest in the orientation shown, what will be is initial angular acceleration? stationary Mf A = total mass= 60 kg 500 Nm 3 m 3 m g
Consider a steel plate of mass m with dimensions L and w that is equally supported by two ball bearings (one on each end of the shaft shown at pointa A and B). At the instant shown below, the plate is released from rest. Part A: Determine an expression for the plate's angular acceleration magnitude a at this in- stant. (Hint: Use Euler's 2nd Law for pinned rotation and the parallel axis theorem.) Part B: Show that the magnitude of the reaction force at each bearing at this instant is R = mg/8. (Hint: Use the kinematics to relate the acceleration of the center of mass G to the angular acceleration. Use Euler's 1st Law to find the reaction forces with the acceleration you determined. As viewed from the side there are two forces acting on the system weight and two reaction forces both pointing upward at the same location.) A foye مر B L २
A 1.6-kg tube AB can slide freely on rod DE which in turn can rotate freely in a horizontal plane. Initially the assembly is rotating with an angular velocity of magnitude w = 5 rad/s and the tube is held in position by a cord. The moment of inertia of the rod and bracket about the vertical axis of rotation is 0.30 kg.m2 and the centroidal moment of inertia of the tube about a vertical axis is 0.0025 kg.m2If the cord suddenly breaks, determine (a) the angular velocity of the assembly after the tube has moved to end E, (b) the energy lost during the plastic impact at E.
3. (17.21) A collar at point C with a mass of 1 kg is rigidly attached at a distance d = 300 mm from the end of a uniform slender rod AB. The rod has a mass of 3 kg and has a length of L = 600 mm. Knowing that the rod is released from rest in the position shown, determine the angular velocity of the rod after it has rotated through 90°. Notes: Ignore rotation of the collar since its dimensions are negligible. The controidal moment of inertia of the rod is I = m[² 12 L d Position 1 Position 1 B B A Position 2 L A' ctivate Windows
7. (a) A uniform prismatic rod of length I and mass m is placed in a vertical position with one end on a smooth horizontal floor. It is then let go, and it falls to the floor from rest in the vertical position. Assuming that the rod never loses contact with the floor, derive an expression for its angular velocity at any position as shown in Figure 7(a). (b) ( =0 Figure 7(a) Determine the height h at which the billiard ball of radius r must be struck so that no frictional force develops between the ball and the table at 4 as shown in Figure 7(b). Assume that the cue only exerts a horizontal force P on the ball. Take IG of the ball equal to (2/5)mr², where m is the mass of the ball. Figure 7(b)
Consider a slender rod AB with a length l and a mass m. The ends are connected to blocks of negligible mass sliding along horizontal and vertical tracks. If the rod is released with no initial velocity from a horizontal position as shown in Fig.A, determine its angular velocity after it has rotated through an angle of θ (see Fig B) using the conservation of energy method. (Hint: Moment of inertia of rod about G = (1/12)ml2 The kinetic energy of a rigid body in plane motion is