Time Interval for Convergence of Angular Positions in Circular Motion

[nik jain]

Homework Statement

Three point particles P , Q , R move in circle of radius r with different but constant speeds . They start moving from their initial position as shown in figure
The angular velocities (in radian/sec) of P , Q , R are 5∏ , 2∏ , 3∏ respectively in the same sense .
The time interval after which they are at same angular position.

The Attempt at a Solution

Let theta be the angle covered by R in time T
T*3∏ = theta + n1∏ (i)
T*2∏ = (∏/2+theta) + n2∏ (ii)
T*5∏ = (∏+theta) + n3∏ (iii)

 

[jbsteele]

From equation (i), (ii) and (iii) we get theta = -n1∏ + n2∏/2 + n3∏ where n1, n2, n3 are integers. Hence, T = (-n1 + n2/2 + n3)/(3∏) The time interval after which they are at same angular position is T.