Mumbai University > Mechanical Engineering > Sem 5 > Theory of Machines-II

Marks: 5 Marks

Year: Dec 2015

Magnitude of Gyroscopic couple:-

Consider a disc spinning at a regular velocity ω about axis of spin OX in anticlockwise direction and viewing from front, shown in fig.

It mean that both position are lying in the same place i.e.- in the precession plane about axis ‘OY’

Let, $\text{I= Mass amount of inertia of the disc about OX in} kg-m^2 \\ \text{W= Angular velocity rad/sec.} \\ \text{Wp= Precession angular velocity rad/sec.}$

Angular momentum of the $disc= I_w$

The change in the angular momentum

$$= \vec{ob} – \vec{oa} = \vec{ab} \\ \vec{ab}= oa \times δθ \\ = I \times W \times δθ$$

Rate of change of angular momentum

$$= I \times W \times \dfrac{δθ}{δt} \\ T = I \times W \times Wp \\ \bigg[\dfrac{δθ}{δt}\bigg]=W_p$$

The couple of I.W.WP is direction of vector with represent the change in angular momentum, which is called as “Active Gyroscopic Couple”.