Question

A disc with radius of gyration of 60 mm as shown in figure below, has a mass of 4 kg. The disc is mounted centrally on a horizontal axle of 80 mm length between the bearings. It spins about the axle at 800 rpm counter clockwise when viewed from the right-hand side bearing. The axle processes about a vertical axis at 50 rpm in the clockwise direction when viewed from above. The resultant reaction at baring at A and B respectively are

• A. 98.6 N upward, 59.4 N downward
• B. 59.4 N downward, 98.6 N upward
• C. 59.4 N upward, 98.6 N downward
• D. None of these

Answer 1

The correct option is B 59.4 N downward, 98.6 N upward


$m=4\text{kg,}N=800\text{rpm,}$
$k=0.06\text{m,}{N}_p=50\text{rpm,}$

$I=m{k}^2=4\times (0.06{)}^2=0.0144{\text{kg.m}}^2$

$l=80mm=0.08m$

$\omega =\frac{2\pi \times 800}{60}=83.78\text{rad/s}$

${\omega }_p=\frac{2\pi \times 50}{60}=5.24\text{rad/s}$

$C=I\omega {\omega }_p=0.0144\times 83.78\times 5.24=6.32\text{N.m}$

Reaction at bearing A due to gyroscopic couple

$=\frac{C}{l}=\frac{6.32}{0.08}=79\text{N (downwards)}$

Reaction at bearing B due to gyroscopic, couple = 79 N (upwards)

$\text{Reactio at each bearing due to weight of teh disc}=\frac{4\times 9.81}{2}=19.6\text{N(upwards)}$
(or)
$\text{Reaction at bearing}A=-79+19.6=59.4N\text{(downwards)}$

$\text{Reaction at bearing}B=79+19.6=98.6N\text{(upwards)}$