The mass of a turbine rotor of a ship is 8000 kg and has a radius of gyration of 0.75 m. It rotates at 1800 r.p.m clockwise when viewed from the stern. Determine the gyroscopic effects in the following cases, (a) If the traveling at 100 km/h steers to the left along a curve of 80 m radius. (b) If the ship is pitching and the bow is descending with maximum velocity. The pitching is with simple harmonic motion with periodic time of 20 s and the total angular movement between the extreme positions is 10°. (c) If the ship is rolling with an angular velocity of 0.03 rad/s clockwise when looking from the stern. In each case,determine the direction in which the ship tends to move.

The mass of a turbine rotor of a ship is 8000 kg and has a radius of gyration of 0.75 m. It rotates at 1800 r.p.m clockwise when viewed from the stern. Determine the gyroscopic effects in the following cases, (a) If the traveling at 100 km/h steers to the left along a curve of 80 m radius. (b) If the ship is pitching and the bow is descending with maximum velocity. The pitching is with simple harmonic motion with periodic time of 20 s and the total angular movement between the extreme positions is 10°. (c) If the ship is rolling with an angular velocity of 0.03 rad/s clockwise when looking from the stern. In each case,determine the direction in which the ship tends to move.

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

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Fluid Kinematics

The branch of science that deals with objects which are either in motion or stationary are studied under the branch of classical mechanics. Fluid mechanics is a subcategory of classical mechanics that deals with the behavior of fluids at rest (fluid statics) or in motion (posing some velocity). In fluid kinematics, studies focus on the associated motion of fluid particles or groups of particles, and its associated parameters like displacements, velocity, and acceleration without concerning about the forces that caused the motion. All the laws of classical mechanics are applied in the study of fluid kinematics.

Question

The mass of a turbine rotor of a ship is 8000 kg
and has a radius of gyration of 0.75 m. It rotates
at 1800 r.p.m clockwise when viewed from the
stern. Determine the gyroscopic effects in the
following cases,
(a) If the traveling at 100 km/h steers to the left
along a curve of 80 m radius.
(b) If the ship is pitching and the bow is
descending with maximum velocity. The pitching
is with simple harmonic motion with periodic time
of 20 s and the total angular movement between
the extreme positions is 10°.
(c) If the ship is rolling with an angular velocity of
0.03 rad/s clockwise when looking from the stern.
In each case,determine the direction in which the
ship tends to move.

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