Rotational motion - i just with net forces

[Linus Pauling]

1. Mass m_1 on the frictionless table of the figure is connected by a string through a hole in the table to a hanging mass m_2.

With what speed must m_1 rotate in a circle of radius r if m_2 is to remain hanging at rest?

http://session.masteringphysics.com/problemAsset/1073602/3/knight_Figure_08_30.jpgp

2. F_radial = mv^2/r
omega = v/r



3. I know that F_z = 0 = normal - mg
What is F_radial? I don't see how to connect the tension caused by m2 to force in the radial direction...

 

[rl.bhat]

If T is the tension in the string, acceleration of m_2 is given by
mg - T = m_2*a.
Similarly write down the expression for m_1. When the system is at rest a = ?

 

[Linus Pauling]

I would have thought m_2*a = t - mg downward. This would not be motion in the radial direction. there is an inward radial force on m1 involving T. it's also obviously connected to m2, but how?

m_1*a = -m_2*T is my intuition but I think it is wrong...

 

[rl.bhat]

The acceleration of both must be zero.
The centripetal force is provided by the tension in the string.
So T = ?
The system will remain at rest it T - mg = ?
Find the values of T from two equations and equate them to get the condition.