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 gyroscop-
ic forces exerted on the bearings by the shaft with a flywheel whose
moment of inertia relative to the rotation axis equals I =
= 3.8.10 3 kg•m 2 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 paral-
lel to the axes of wheels. The turbine's rotation direction coincides
with that of wheels. The moment of inertia of the turbine rotor rel-
ative to its own axis is equal to I = 240 kg• m 2. Find the additional
force exerted by the gyroscopic forces on the rails when the locomo-
tive 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 longitudi-
nal 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.
1 dV
0= --17- dp • (1.6d)
- Volume density of elastic strain- energy:
u = E8 2 /2, u = Gy 2 /2. (1.6e)
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