A huge vertical pump configuration, comprised of onesolid disc A and two solid rotors B, is started from restwith a motor drive that delivers torque as a functionof time. Determine (a) the total mass moment ofinertia in kg-m^2, (b) the angular velocity in RPM 45seconds after starting from rest and (c) the number ofrevolutions in that same time period. The mass andradius of disk A are 29800 kg and 2.8 m and same forone rotor B are 1100 kg and 0.3 m. The torque vstime function is: T = 8.4E4 t ^(0.35) N-m.B2980011002.80.38.40.3545

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Answered: A huge vertical pump configuration,…

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter11: Dynamics Of Rigid Bodies

Section: Chapter Questions

Problem 11.31P

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Similar questions

A uniform sphere of mass m and radius R rolls without slipping down a plane at an angle θ from thehorizontal. Show that the acceleration along the slope of the center of mass is aCM = (5/7)g sin θ and that the force of static friction needed is fs = (2/7)mg sin θ. What minimum coefcient of friction µs is needed to satisfythe conditions of the problem?
. A cylinder of mass M, of radius R, and of lengthL such that, L = 6R is hinged at point A in verticalposition. It suddenly starts to rotate about thehinge at A with an initial angular speed of wo.Determine the support reactions at A in normaland tangential directions when the cylinder is inhorizontal position.
Calculate the moment of interim Ip of the disk( without the point mass) with respect to point P, in terms of M and R. Ip=?
At the moment of impact, the line of the centers of the sphere is perpendicular to a vertical wall which is at a distance x from the point of collision and nearer(closer) to B than to A, and B subsequently collides with the wall. Find in terms of x, the distance of A from the wall at the instant when B hits the wall.
(Please explain)In a collision of disks, where the system is not isolated because of the existence of friction. How is it possible that conservation of angular momentum is still valid to a relatively good accuracy?
Please explain. In the collision of disks, the system is not isolated because of existence of friction.How is it possible that conservation of angular momentum is still valid to a relativelygood accuracy?
The two balls are attached to the light rigid rod, which is suspended by a cord from the support above it. If the balls and rod, initially at rest, are struck with the force F = 11.5 lb, calculate the magnitudes of the corresponding acceleration of the mass center and the rate at which the angular velocity of the bar is changing.
Consider the case of a rotating wheel at rest and starting a clockwise rotation, meaning the negative direction of the angular velocity, and increasing (negatively) its value up to -12 rad/sec for 2 seconds. It then maintains a constant velocity for 2 seconds, and then uniformly reduces the magnitude of the velocity for 2 seconds until the wheel is momentarily stopped and restarts its rotation counter-clockwise with positive angular velocity, accelerating up to 20 rad/sec in 2 seconds and remaining at a constant rotation for 2 more seconds. Finally, the wheel stops gradually in 2 seconds. Next, you can see the graph of angular velocity versus time of this rotation: Apply the angular position equation. with θo=0, wo=0, substituting the value of the angular acceleration in the range from 0 to 2 seconds obtained in question 2, perform the tabulation of values to fill the following table; describe the type of parabola and draw the graph: Equation:θ=f(t) Concavity type:…
Consider the case of a rotating wheel at rest and starting a clockwise rotation, meaning the negative direction of the angular velocity, and increasing (negatively) its value up to -12 rad/sec for 2 seconds. It then maintains a constant velocity for 2 seconds, and then uniformly reduces the magnitude of the velocity for 2 seconds until the wheel is momentarily stopped and restarts its rotation counter-clockwise with positive angular velocity, accelerating up to 20 rad/sec in 2 seconds and remaining at a constant rotation for 2 more seconds. Finally, the wheel stops gradually in 2 seconds. Next, you can see the graph of angular velocity versus time of this rotation: Find the angular acceleration in the range from 10 to 12 seconds by applying the corresponding rotational kinematics equation and write the equation as a function of angular velocity with respect to time. Write the results below:
Consider the case of a rotating wheel at rest and starting a clockwise rotation, meaning the negative direction of the angular velocity, and increasing (negatively) its value up to -12 rad/sec for 2 seconds. It then maintains a constant velocity for 2 seconds, and then uniformly reduces the magnitude of the velocity for 2 seconds until the wheel is momentarily stopped and restarts its rotation counter clockwise with positive angular velocity, accelerating up to 20 rad/sec in 2 seconds and remaining at a constant rotation for 2 more seconds. Finally, the wheel stops gradually in 2 seconds. Next you can see the graph of angular velocity versus time of this rotation: Get the slope of the straight line in the range from 4 to 6 seconds and use analytical geometry to build the equation of that line, in the slope-intercept equation form.
You are the technical consultant for an action-adventure film in which a stunt calls for the hero to drop off a 19-m-tall building and land on the ground safely at a final vertical speed of 5 m/s. At the edge of the building's roof, there is a 100-kg drum that is wound with a sufficiently long rope (of negligible mass), has a radius of 0.4 m, and is free to rotate about its cylindrical axis with a moment of inertia I0. The script calls for the 76-kg stuntman to tie the rope around his waist and walk off the roof. (a) Determine an expression for the stuntman's linear acceleration in terms of his mass m, the drum's radius r, and moment of inertia I0. (b) Determine the required value of the stuntman's acceleration if he is to land safely at a speed of 5 m/s.
Check Your Understanding Which has greater angular momentum: a solid sphere of mass m rotating at a constant angular frequency 0 about the z-axis, or a solid cylinder of same mass and rotation rate about the z-axis?

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