Circular Motion Question

• Mar 2nd 2010, 03:26 PM
craig
Circular Motion Question
2 Particles, having mass of $m$ and $2m$ respectively are connected by a light inextensible string, threaded through a fixed smooth ring. The lighter particle moves uniformly around a horizontal circle radius of radius $r$, while the other particle remains at rest.

Find the speed of the lighter particle?

No idea how start this, I've dealt with a bit of circular motion but not sure how to relate it to the mass of the particles?

Thanks in advance for any help
• Mar 2nd 2010, 05:39 PM
qmech
In order for the lighter particle to be moving in a circle, it has to be experiencing acceleration towards the center of the circle with magnitude mv^2/r. That acceleration is supplied by the heavier particle trying to respond to gravity, i.e., (2m)g. These 2 accelerations are equal.
• Mar 3rd 2010, 11:00 AM
craig
Quote:

Originally Posted by qmech
In order for the lighter particle to be moving in a circle, it has to be experiencing acceleration towards the center of the circle with magnitude mv^2/r. That acceleration is supplied by the heavier particle trying to respond to gravity, i.e., (2m)g. These 2 accelerations are equal.

Thank you, that's surprisingly easy...

Accelerations are equal, therefore $\frac{mv^2}{r} = 2mg$

Cancelling out the masses and multiplying through by r, we get $v^2 = 2gr$, so $v = \sqrt{2gr}$?

Thanks again for the quick reply
• Mar 3rd 2010, 11:27 AM
craig
Would the larger particle have an acceleration though if it remains stationary? Would have thought that this would be zero?