Question

Two small rings O and O' are put two vertical stationary rods AB and A'B', respectively. One end of an inextensible thread is tied at point A'. The thread passes through ring O' and its other end is tied to ring O. Assuming that the ring O' moves downwards at a constant velocity $V_1$ determine the velocity $V_2$ of the ring when $\angle AO{O}^{\prime }=\alpha$

Answer 1

Let us go over to the reference frame fixed to ring $O^{{}^{\prime }}$ In this system the velocity of ring $O$ is ${\nu }_1/\cos \alpha$ and is directed upwards since the thread is inextensible, and i pulled at a constant velocity ${\nu }_1$ relative to ring $O^{{}^{\prime }}$ Therefore the velocity of ring $O$ relative to the straight line $A{A}^{{}^{\prime }}$ (which is stationary with respect to the ground)is
${\nu }_2=\frac{{\nu }_1}{\cos \alpha }-{\nu }_1={\nu }_1\frac{2{\sin }^2\left(\alpha /2\right)}{\cos \alpha }$
an dis directed upwards