Question

A horizontal axle AB, 1 m long, is pivoted at the
mid point C. It carries a weight of 20 N at A and
a wheel weighing 50 N at B. The wheel is made
to spin at a speed of 600 r.p.m. in a clockwise
direction looking from its front. Assuming that
the weight of the flywheel is uniformly distributed
around the rim whose mean diameter is 0.6 m
calculate the angular velocity of precession of
the system around the vertical axis through​

Answer 1

Answer:

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Answer 2

Given that :

Length of the axle, L= 1m (from A to B)

Load at A, Fa= 20N ;   Load at B (wheel), Fb= 50N ;

Angular velocity, w = 600rpm = 62.83 rad/s;   Diameter = 0.6m, Radius = 0.3m

Step 1 :

Draw FBD to calculate the resultant moment of the axle. (center pivoted)

M= 50(0.5)-20(0.5) = 15 Nm

therefore gyroscopic couple, C = M = 15Nm

Step 2:

Gyroscopic couple = moment of inertia x angular velocity x precession

                            15  = (50/9.81)(0.3)^2 x 62.83 x precession

               Precession= 0.52 rad/s

*moment of inertia= moment of inertia of the flywheel at point B.