The distance between the bearings in which the axle of the disc is
mounted is equal to 1 = 15 cm. The axle is forced to oscillate about
a horizontal axis with a period T = 1.0 s and amplitude cpm, = 20°.
Find the maximum value of the gyroscopic forces exerted by the axle
on the bearings.
1.288. A ship moves with velocity v = 36 km per hour along an
arc of a circle of radius R = 200 m. Find the moment of the gyroscopic forces exerted on the bearings by the shaft with a flywheel whose
moment of inertia relative to the rotation axis equals I =
= 3.8.103 kg•m2 and whose rotation velocity n = 300 rpm. The
rotation axis is oriented along the length of the ship.
1.289. A locomotive is propelled by a turbine whose axle is parallel to the axes of wheels. The turbine's rotation direction coincides
with that of wheels. The moment of inertia of the turbine rotor relative to its own axis is equal to I = 240 kg• m2. Find the additional
force exerted by the gyroscopic forces on the rails when the locomotive moves along a circle of radius R =- 250 m with velocity v =
50 km per hour. The gauge is equal to / = 1.5 m. The angular
velocity of the turbine equals n = 1500 rpm.
1.6. ELASTIC DEFORMATIONS OF A SOLID BODY
• Relation between tensile (compressive) strain a and stress a:
= alE,
(1.6a)
where E is Young's modulus.
• Relation between lateral compressive (tensile) strain a' and longitudinal tensile (compressive) strain a:
a' = —lie,
(1.6b)
where p, is Poisson's ratio.
• Relation between shear strain y and tangential stress t:
y = 't/G,
(1.6c)
where G is shear modulus.
• Compressibility:
1 dV
0= --17- dp •
(1.6d)
• Volume density of elastic strain- energy:
u = E82/2, u = Gy2/2.
(1.6e)
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