How Long to Achieve 1-g Environment in a Rotating Space Cylinder?

[ScottM]

Homework Statement

I'm a Physics I student and having a difficult time with this problem. I feel like I'm missing something obvious but at this point I've put in too much time and I'm ready to ask for help. The problem is, it involves the use of radians as the measure of angular speed and I'm not all that familiar with radians. It's been a long time since I've taken trig (15 years), so I'm guessing this problem is a lot easier than I think. Anyway, here's the problem:

To maintain their bone density and other vital bodily signs, the inhabitants of a cylindrically shaped living space want to generate "1-g environment" on their way to a distant destination. Assume the cylinder has a diameter of 250 m (they live on the inner surface) and is initially not rotating about its long axis. For minimal disruption, the constant angular acceleration is a very gentle .00010 rad/sec-squared. Determine how long it takes for them to reach their goal of a "1-g environment."

I can't see how this done without knowing the mass. I've tried to find an equality with mass on both sides to cancel out, but no luck. I'm having some difficulty with the concepts of angular and tangential speed (specifically the right hand rule, the book does a terrible job of explaining it) as well.

Thanks - Scott

Homework Equations

The Attempt at a Solution

 

[andrevdh]

The spinning cylinder will give its occupants a centripetal acceleration (inwards towards the axis of rotation). The (angular) speed of the drum need to be such that the centripetal acceleration is equal to g (gravitational acceleration)

$$a_c = g = \frac{v^2}{r}$$

The relationship between angular speed of a rotating object and its speed is given by

$$v = \omega r$$

if you substitute this into the equation you will find that the only unknown is the angular speed. You need to find the relation between the angular speed, angular acceleration and time in order to calculate the required time for the cylinder to reach the angular speed that will give the occupants a centripetal acceleration of g.

 

[feryxx]

the angular velocity when the gravitational acceleration is vanished

 

[ashishsinghal]

the angular velocity when the gravitational acceleration is vanished

What do you want to say? I did not understand your post.