Converting angual velocity to linear velocity

[crybllrd]

Homework Statement

An astronaut is being tested in a centrifuge. The centrifuge has a radius of 10m and, in starting, rotates \theta=0.30t^{2}, there t is in seconds and \theta in radians. When t=5.0s, what are the magnitudes of the astronaut's (a) angular velocity, (b) linear velocity, (c) tangential acceleration, and (d) radial acceleration?

Homework Equations

Kinematics equations

The Attempt at a Solution

For (a), I used \theta=.30(5)^{2}=7.5rad, plugging in 5.0s for t. Then knowing initial angular velocity = 0, time = 5s, and now \theta=7.5rad, I used a kinematics equation to determine final angular velocity to be 3rad/s.

Part (b) is where I'm stuck. I was thinking to convert 3 rad/s to degrees, then divide by 360 degrees to get 4.7 rotations a second, but not sure where to go from there (or if I'm on the right track).

 

[rock.freak667]

Well you can formulate the expression for v using v=rω and you know that ω=dθ/dt.

 

[crybllrd]

Thanks for the fast reply.
Where does that leave me in units? Seems like it would be (rad*m)/s. Is there a way I can divide out the radians?

 

[rock.freak667]

Thanks for the fast reply.
Where does that leave me in units? Seems like it would be (rad*m)/s. Is there a way I can divide out the radians?

a radian is the ratio of arc length to radius so essentially, you can leave out the radian with no consequence.