Find the tensions in the strings

[MyNewPony]

Homework Statement

Two objects of equal mass m are whirling around a shaft with a constant angular velocity ω. The first object is a distance d from the central axis, and the second object is a distance 2d from the axis. You may assume the strings are massless and inextensible. You may ignore the effect of gravity. Find the tensions in the two strings.

Homework Equations

F(net) = ma
α = ω^2*r
a = αr

The Attempt at a Solution

First string:

If gravity is ignored, the only force acting on the object is tension. Thus,

T = ma

and

T = m(ω^2*d^2)

Second string:

T = ma

and

T = m(ω^2*(2d)^2)
T = m(ω^2*4d^2)

Are there any other forces acting on the objects?

 

[poopcaboose]

Well you know that the tension will oppose the centripetal acceleration and that the centripetal force will equal the tension. Therefore you are close T=m(w^2*r) where w means omega, or angular velocity, and r is the radius. Just don't square the radius it gets canceled out in the math.

 

[LowlyPion]

Your tangential acceleration |a| is related to |α|*r.

But a is not directed along the string. They are orthogonal. It's α that is directed along the string.

The tension in the string then is given simply by

T = m*ω²*r