User talk:Vizimin

Point masses $$ A $$ and $$B$$ move anticlockwise with same speed $$v$$  in a circle of radius $$R$$ and are initially diametrically opposite to each other. At $$t=0$$ $$A$$  is given constant acceleration at $$72 v^2/25\pi R $$. Calculate the time in which$$A$$ collides with $$B$$, angle traced by $$A$$, its angular velocity and radial acceleration at time of collision.

Answer

Since they are diametrically opposite, the initial distance of separation is $$S= \pi R $$. Plugging this into $$S = \frac{1}{2} a t^2 $$, with $$a = 72 v^2/25\pi R $$, we get $$t= \frac{5 \pi R} {6v}$$.

Angle traversed:

$$S = u t +\frac{1}{2} a t^2 = v \frac{5 \pi R} {6v} + \frac{1}{2} (72 v^2/25\pi R) \left(  \frac{5 \pi R} {6v}\right)^2 = \frac{11 \pi R }{6} $$

Angle $$\theta = S/R = \frac{11 \pi }{6}$$

Angular velocity:

$$v'/R = u/R + at/R = (17 v/ 5R)$$