A uniform disc of diametermm and of mass 5 kg is mounted on one end of an arm of lengthmm. The other end of the arm is free to rotate in a universal bearing. If the disc rotates about the arm with a speed ofr.p.m. clockwise, looking from the front, with what speed will it precess about the vertical axis?
a) 14.7 rad/s
b) 15.7 rad/s
c) 16.7 rad/s
d) 17.7 rad/s
Q.2.
An aeroplane makes a complete half circle ofmetres radius, towards left, when flying atkm per hr. The rotary engine and the propeller of the plane has a mass ofkg and a radius of gyration of 0.3 m. The engine rotates atr.p.m. clockwise when viewed from the rear. Find the gyroscopic couple on the aircraft.
a) 10.046 kN-m
b) 11.046 kN-m
c) 12.046 kN-m
d) 13.046 kN-m
Q.3.
The turbine rotor of a ship has a mass of 8 tonnes and a radius of gyration 0.6 m. It rotates atr.p.m. clockwise, when looking from the stern. Determine the gyroscopic couple, if the ship travels atkm/hr and steer to the left in a curve ofm radius.
a) 100.866 kN-m
b) 200.866 kN-m
c) 300.866 kN-m
d) 400.866 kN-m
Q.4.
The heavy turbine rotor of a sea vessel rotates atr.p.m. clockwise looking from the stern, its mass beingkg. The vessel pitches with an angular velocity of 1 rad/s. Determine the gyroscopic couple transmitted to the hull when bow is rising, if the radius of gyration for the rotor ismm.
a) 4.364 kN-m
b) 5.364 kN-m
c) 6.364 kN-m
d) 7.364 kN-m
Q.5.
The turbine rotor of a ship has a mass ofkg. It has a radius of gyration of 0.m and a speed ofr.p.m. clockwise when looking from stern. Determine the gyroscopic couple upon the ship when the ship is steering to the left on a curve ofm radius at a speed ofkm/h.
a) 11.27 kN-m
b) 22.27 kN-m
c) 33.27 kN-m
d) 44.27 kN-m
Q.6.
The turbine rotor of a ship has a mass ofkg. It has a radius of gyration of 0.m and a speed ofr.p.m. clockwise when looking from stern. Determine the gyroscopic couple upon the ship when the ship is pitching in a simple harmonic motion, the bow falling with its maximum velocity. The period of pitching isseconds and the total angular displacement between the two extreme positions of pitching isdegrees.
a) 3.675 kN-m
b) 4.675 kN-m
c) 5.675 kN-m
d) 6.675 kN-m
Q.7.
The mass of the turbine rotor of a ship istonnes and has a radius of gyration of 0.m. Its speed isr.p.m. The ship pitchesabove andbelow the horizontal position. A complete oscillation takesseconds and the motion is simple harmonic. Determine Maximum gyroscopic couple.
a) 11.185 kN-m
b) 22.185 kN-m
c) 33.185 kN-m
d) 44.185 kN-m
Q.8.
The mass of the turbine rotor of a ship istonnes and has a radius of gyration of 0.m. Its speed isr.p.m. The ship pitchesabove andbelow the horizontal position. A complete oscillation takesseconds and the motion is simple harmonic. Determine Maximum angular acceleration of the ship during pitching.
a) 0.0016 rad/s2
b) 0.0026 rad/s2
c) 0.0036 rad/s2
d) 0.0046 rad/s2
Q.9.
A ship propelled by a turbine rotor which has a mass of 5 tonnes and a speed ofr.p.m. The rotor has a radius of gyration of 0.5 m and rotates in a clockwise direction when viewed from the stern. Find the gyroscopic effect when the ship sails at a speed ofkm/h and steers to the left in a curve havingm radius.
a) 38.5 kN-m
b) 48.5 kN-m
c) 58.5 kN-m
d) 68.5 kN-m
Q.10.
A ship propelled by a turbine rotor which has a mass of 5 tonnes and a speed ofr.p.m. The rotor has a radius of gyration of 0.5 m and rotates in a clockwise direction when viewed from the stern. Find the gyroscopic effect when the ship pitches 6 degree above and 6 degree below the horizontal position. The bow is descending with its maximum velocity. The motion due to pitching is simple harmonic and the periodic time isseconds.
a) 6075 N-m
b) 7075 N-m
c) 8075 N-m
d) 9075 N-m
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