At t=0 the angular velocity of the mass is  and the string breaks.  For later times a force acts which keeps the angular velocity  constant at .  The force has no radial component, i.e., .  Find .

 

First, write Newton’s second law:

(0.1)

 But,  so

(0.2)

The first equation is easily solved:

(0.3)

and so

(0.4)

 

where a and b are constants to be determined.  Since  and , it is easy to show that .  Therefore

(0.5)

Since ,

(0.6)

Finally, from the equation (0.2) for F,

.

(0.7)

 

 

 

Early trajectory of m for R₀=1

 

 

Trajectory of m for R₀=1 over 360⁰ (note log scale for r)