The mass of the turbine rotor of a ship is 20 tonnes and has a radius of gyration of 0.60 m. Its speed is 2000 r.p.m. The ship pitches 6° above and 6° below the horizontal position. A complete oscillation takes 30 seconds and the motion is simple harmonic. Determine Maximum angular acceleration of the ship during pitching.

Question

The mass of the turbine rotor of a ship is 20 tonnes and has a radius of gyration of 0.60 m. Its speed is 2000 r.p.m. The ship pitches 6° above and 6° below the horizontal position. A complete oscillation takes 30 seconds and the motion is simple harmonic. Determine Maximum angular acceleration of the ship during pitching.

asked Sep 22, 2022 in Machine Dynamics by Grayson (34.3k points)

The mass of the turbine rotor of a ship is 20 tonnes and has a radius of gyration of 0.60 m. Its speed is 2000 r.p.m. The ship pitches 6° above and 6° below the horizontal position. A complete oscillation takes 30 seconds and the motion is simple harmonic. Determine Maximum angular acceleration of the ship during pitching.

(a) 0.0016 rad/s^2

(b) 0.0026 rad/s^2

(c) 0.0036 rad/s^2

(d) 0.0046 rad/s^2

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This intriguing question originated from Effect of Gyroscopic Couple on an Aeroplane in portion Gyroscopic Couple and Precessional Motion of Machine Dynamics

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Fred · Answer 1 · 2022-10-14T00:36:48+0000

Right option is (d) 0.0046 rad/s^2

For explanation: We know that maximum angular acceleration during pitching

= φ(ω1)^2 = 0.105 (0.21)^2 = 0.0046 rad/s^2

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