Circular Motion probem - 3

Tension is a force and force is related to acceleration via Newton's 2nd law. How do you determine the acceleration of a particle moving in a circle at constant angular speed ##\omega##?

Draw free-body diagrams for each mass. You need to consider the NET force acting on each particle.

 

Since the only forces acting on the particles are tensions which are radial ,there will be no tangential acceleration.

The FBD in the above post#4 is incorrect.

Let the tension in the string OA be T1,AB be T2 and BC be T3.The length of each string segment be l.

Now for A, T1-T2=mv₁²/l

For B ,T2-T3=mv₂²/2l

Similarly you can write eq for C.

From this you will get the desired ratio.