A solid circular steel disc 250mm diameter and 50 mm thick is mounted with its polar axis on the line OX, of the three Cartesian axes OX, OY and OZ. If at a particular instant the disc is snipping about OX at 12 rad/sec in anticlockwise direction when viewed from right hand side and the frame is rotated at 5 rad/sec magnitude and sense of the gyroscopic couple. Density of the steel may be taken as 7.8 gm/cc. -

Given:

ρ = 7.8 gm/cc

D = 250mm = 25cm = 0.25m

T = 50mm = 5cm

W= 12 rad/s

Wp = 5 rad/s

Formula:

C = I w wp

Solution:

Finding volume V $= π D^2 /4 \times T \\ = 3.14 \times 252 / 4 \times 5 \\ 2453 cc$

Finding mass:

M $= ρ \times V \\ = 7.8 \times 2453 = 19134 grams \\ = 19.13 kg$

Finding M.I

I $= mr^2/2 \\ = 19.13 x 0.1252 / 2 = 149.5 kgm2$

Finding gyroscopic couple

C $= I w wp \\ = 149.5 \times 12 \times 5 = 8969 Nm$

It will act in the direction as shown in the following figure.