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- In the helicopter shown; a vertical tail propeller is used to pre- vent rotation of the cab as the speed of the main blades is changed. Assuming that the tail propeller is not operating determine the final angular velocity of the cab after the speed of the main blades has been changed from I80 to 240 rpm. (The speed of the main blades is measured relative to the cab, and the cab has a centroidal moment of inertia of 650 lb.ft.s2. Each of the four main blades is assumed to be a slender rod 14 ft weighing 55 lb.)The mass of flywheel of an engine is 8 tonnes and the radius of gyration is 1.8 metres. It is found from the turning moment diagram that the fluctuation of energy is 100 kN-m. If the mean speed of the engine is 150 r.p.m., find the maximum and minimum speeds.5) In ice figure skating, a couple execute a “top” (see picture). The centre of mass of the woman (58 kg) is situated 1.3 m from the axis of rotation which is vertical and passes through the centre of mass of the man (85 kg). They are spinning at a constant angular velocity equal to 3.1415 rad/s and the man and woman have moments of inertia, about their own centres of mass, equal to 1.6 and 2.5 kg.m2 respectively. Then the woman grabs the neck of the man. At this point, her moment of inertia decreases to 1.4 kg.m2 and her body centre of gravity is 0.9 m from the axis of rotation. Determine the new angular velocity. Hints: This is a conservation of angular momentum problem, and needs the parallel axis theorem to determine moments of inertia about the axis of rotation. The skaters are moving as one body with one angular velocity, but they each have their own moments of inertia given relative to their own CoMs. For the man, that’s fine…the axis they’re rotating about passes through his…
- a rotating shaft carries four unbalanced masses 18 kg, 14 kg, 16 kg and 12 kg at radii 50 mm, 60 mm, 70 mm and 60 mm respectively. the 2nd, 3rd and 4th masses revolve in planes 80 mm, 160 mm and 280 mm respectively measured from the plane of the first mass and are angularly located at 60°, 135° and 270° respectively measured clockwise from the first mass looking from this mass end of the shaft. the shaft is dynamically balanced by two masses, both located at 50 mm radii and revolving in planes mid-way between those of 1st and 2nd masses and midway between those of 3rd and 4th masses. determine, graphically or otherwise, the magnitudes of the masses and their respective angular positions.In the figure shown, the hydraulic cylinder moves upwards with a constant speed of Va=0.2 m/s, transferring vertical movement to corner A of the container. If bearing b never slips and has a diameter of 8 cm, determine the angular velocity of the imaginary line drawn from its axis of rotation to any point on its periphery. Determine the angular velocity of side CD at this moment.Prove the relation that Hammer blow = ± mb x r*x ω2 where mb = Balancing mass placed at a radius of r* and ω= angular speed of the crank.
- A rotating shaft carries four unbalanced masses 18 kg, 14 kg, 16 kg and 12 kg at radii 50 mm, 60 mm, 70 mm and 60 mm respectively. The 2nd, 3rd and 4th masses revolve in planes 80 mm, 160 mm and 280 mm respectively measured from the plane of the first mass and are angularly located at 60°, 135° and 270° respectively measured clockwise from the first mass.The shaft is dynamically balanced by two masses, both located at 50 mm radii and revolving in planes mid-way between those of 1st and 2nd masses and midway between those of 3rd and 4th masses. Determine, balancing mass by drawing couple polygon and their respective angular position graphically.An aeroplane makes a complete half circle of 70 metres radius, towards left, when flying at 500 km per hr. The rotary engine and the propeller of the plane has a mass of 600 kg and a radius of gyration of 0.3 m. The engine rotates at 2500 r.p.m. clockwise when viewed from the rear. Find the gyroscopic couple on the aircraft.Determine the gyroscopic couple, if the ship travels at 2 km/min and steer to the right in a curve of 65 m radius.The turbine rotor of a ship has a mass of 10tonnes and a radius of gyration 1.5 m. It rotates at 38r.p.s. anticlockwise, when looking from the stern and write the reactive gyroscopic effect.
- At the top A of the vehicle moving along line AC in the figureIts speed is 30 m / sec and its weight is 9 kN.Tool radius of curvature 40The reaction force to the tires when reaching point B, which is m,and so that the tires do not separate from the asphalt when it reaches point CWhat should be the radius of curvature of point C? (hA = 6 m andhC = 9 m)A stepped cylinder has the dimensions R₁ = 0.30 m, R₂ = 0.65 m, and the radius of gyration, k, is 0.35 m. The mass of the stepped cylinder is 100 kg. Weights A and B are connected to the cylinder. If weight B has a mass of 80 kg, and weight A has a mass of 50 kg, how far does A move in 5 seconds? In which direction does it move? (Draw all FBDs)A motorcycle and rider have a combined mass of 350kg. The each wheel has a mass of 20kg with the diameter of 500 mm. The rider accelerates from 5m/s to 25m/s over a distance of 100m, whilst climbing a hill of slope 1 in 20. Identify the magnitude and effect of gyroscopic reaction torque by calculating the angular velocity and power as the motorcycle ascends the incline when the motorcycle and rider travel at 80 km/h around a left-hand bend of road with the radius 30 m.Explain the effects of energy transfer in mechanical systems (e.g. gears, pulley or flywheel) with uniform acceleration present.