Newtonian mechanics

[kolahal_b]

Two particles of mass m and M aunergo uniform circular motion. abput each other at a separation R under the influence of attractive force F.The angular velocity is w rad/s

Show that R=(F/w^2)(1/m+1/M)

My approach gives R=(2F/w^2)(1/(m+M))

[Tim_Lou]

relative to the center of mass:

[math]R=R_1+R_2[/math]

 

[math]mR_1=MR_2[/math]

 

[math]R=R_1(1+\frac{m}{M})[/math]

 

since [math]F=mv^2/R_1=mw^2R_1[/math]

 

substitute...... it turns out that the first one is correct... perhaps you forgot to take the reference at the center of mass?

[kolahal_b]

You are taking the centre of mass, and using F=m(w^2)R1

But my question was the two masses execute uniform circular motion about one nother.Please don't mind, I feel difficult to visualise that the masses revolves around the C.M. rather than others' centres.