EXERCISE 5.1 Spheres A and B are welded to a connecting bar of negligible mass that is mounted obliquely on a shaft that rotates at the constant rate . The mass of the shaft also is negligible, so the center of mass O of this system is situated on the shaft. Thus the system is statically balanced. Evaluate the angular momentum of the two spheres about the center of mass in a stationary frame when the connecting bar is horizontal and when the shaft has rotated by 1° from that position. (Hint: Use O as the origin of frame XYZ. The direction of X is along the shaft. Z direction is vertically upward. Attach frame xyz to the bar and make it coincide with frame XYZ at the instant.)

EXERCISE 5.1 Spheres A and B are welded to a connecting bar of negligible mass that is mounted obliquely on a shaft that rotates at the constant rate . The mass of the shaft also is negligible, so the center of mass O of this system is situated on the shaft. Thus the system is statically balanced. Evaluate the angular momentum of the two spheres about the center of mass in a stationary frame when the connecting bar is horizontal and when the shaft has rotated by 1° from that position. (Hint: Use O as the origin of frame XYZ. The direction of X is along the shaft. Z direction is vertically upward. Attach frame xyz to the bar and make it coincide with frame XYZ at the instant.)

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

5. An 80 kg gymnast dismounts from a high bar. He starts the dismount at full extension, then tucks to complete a number of revolutions before landing. His moment of inertia when fully extended can be approximated as a rod of length 1.8 m and when in the tuck a rod of half that length. If his rotation rate at full extension is 1.0 rev/s and he enters the tuck when his center of mass is at 3.0 m height moving horizontally to the floor, how many revolutions can he execute if he comes out of the tuck at 1.8 m height? High bar 1.8 m 3 m ANS. Moment of inertia at full extension, I = 21.6 kg-m^2 Moment of inertia at the tuck I' = 5.4 kg-m^2 Angular velocity at the tuck = 4 rev/sec Time interval in the tuck = 0.5 sec i.e. In 0.5 s, he will be able to execute two revolutions at 4.0 rev/s.
The uniform thin pin-connected bars AB, BC, and CD have masses mÃß = 2.3 kg, mBC = 3.2 kg, and mCD= 5.0 kg, respectively. Letting R = 0.75 m, L = 1.2 m, and H= 1.55 m and knowing that bar AB rotates at a constant angular velocity WAB= 4 rad/s, compute the angular momentum of bar AB about A, of bar BC about A, and bar CD about D at the instant shown. R L B WAB + | Do H The angular momentum of bar AB about A is ( The angular momentum of bar BC about A is ( The angular momentum of bar CD about Dis ( kg.m²/s) k. kg-m²/s) k. kg-m²/s) k.
P.3) Determine the angular momentum Hp for the three masses A, B, and C (mA = mB = mc = 0.2 kg) when all three masses are clustered at the origin O of the Cartesian coordinate axes. The point P is located at 0.1 m away from the origin in k direction. The velocities of the masses are; VA = 0.05 i m/s, VB = 0.05 j m/s, and vc 0.05 km/s. X k
bucket of mass m is hanging from the free end of a rope whose other end is wrapped around a drum (radius R, mass M) that can rotate with negligible friction about a stationary horizontal axis. The drum is not a uniform cylinder and has unknown moment of inertia. When you release the bucket from rest, you find that it has a downward acceleration of magnitude a. What are (a) the tension in the cable between the drum and the bucket and (b) the moment of inertia of the drum about its rotation axis?
A gum with mass m is attached to the rim of a disk with mass M and radius R The disk and the gum Is Initlally rotating with angular speed w around an axis which passes through the center of the disk and is perpendicular to the plane of the disk as shown in the figure. At a certain instant the gum breaks loose and flies off with a speed of v. Which of the followings gives the correct expression for the final angular speed w of the disk. (Igum = mR, Iatak = MR /2) %3D %3D Select one: Mv 2m 1+ M O a. 2mR M. ). 2mv 2m 1+ M O b. - MR 2Mv 2M 1+ :), • d. (1+) - mR MR mv O e. 1+ 2M - 2MR
1) Three small spheres are rigidly mounted to a horizontal shaft with rotates with angularvelocity omega as shown. Neglect sphere radii, ignore gravity. Spheres have masses m1, m2andm3 as shown.a. What is the angular momentum HO about O the center of the coordinates shown?b. At this instant, what is Ax , the x component of the bearing force at A to offset the dynamicimbalance? Note that you are NOT asked to find any other forces (Ay, Ox, or Oy) in interestof time.
For the three scenarios shown below, determine the angular velocity about point O, if each rigid body has the same angular momentum of 0.1 kg-m²/s. System 1: r = 45 cm, m = 600 g. System 2: rod L = 90 cm, m = 350 g. System 3: rod length, d = 67 cm, m = 630 g. (0) 00₂ L2 G L2 2 3 2 G
P.3) Determine the angular momentum Hp for the three masses A, B, and C (ma = mB = mc 0.2 kg) when all three masses are clustered at the origin O of the Cartesian coordinate axes. The point P is located at 0.1 m away from the origin in k direction. The velocities of the masses are; VA = 0.05 i m/s, vB = 0.05 į m/s, and vc = 0.05 k m/s. CB P
A slender rod of mass mo and length ; is welded at its idpoint A to the rim of the oslid circular disk of mass m and radius r. the center of the disk, which rolls without slipping, has a velocity v at the instant when A is at the top of the disk with the rod parallel to the ground. For the instant determine the angular momentum of the combined body about O. The angular momentum is positive if counterclockwise, negative if clockwise.
Calculate the linear momentum (L) of a motor car wheel which has a radius of gyration (kG) = 550 mm, diameter 10 m and mass = 7.5 kg. The wheel is moving at an angular velocity, @= 3.5 rad's. 12.60 N.s OB 10.50 N.s. 13.13 N.s 11.70 N.s
ASAP
In the system shown, the two masses (of m-kg and 5-m kg) are connected by a cable wrapped around a double pulley (of inner radius R, and outer radius 2R) , and that has a radius of gyration R and mass m. If the system is released from rest with the spring in the unstretched position (consider the spring to be upstretched when x=0) (a) Write an expression for the kinetic energy and potential energy of the system at any given position x (b) What is the velocity vof the mass on the left (the m-kg mass)?at any position xin terms of the parameters given, (In terms of the given parameters, m, x, g, k, and R) (C) What is the maximum velocity of the mass on the left (the m-kg mass)?, If m=6.1-kg. , g=9.81, ku112-N/m, and R=0.1 v, X k R m 2R- g 5m