# Angular Velocity of a centrifuge

1. Mar 24, 2005

### BJN153

An astronaut is being tested in a centrifuge. The centrifuge has a radius of 10.5 m and, in starting, rotates according to Θ(theta) = 0.13t^2, where t in seconds gives Θ in radians. When t = 5.0 s, what are the astronaut's angular velocity?
What is the astronauts linear speed?
What is the astronauts tangential acceleration (magnitude only)?
What is the astronauts radial acceleration (magnitude only)?

2. Mar 24, 2005

### whozum

By deriving:

$$\theta(t) = .13t^2$$ <-- Position Function
$$\omega(t) = .26t$$ <-- Velocity Function
$$\alpha(t) = .26$$ <-- Acceleration Function

Find the angular accelerations and speeds, then think of a relationship between the angular accel/speed and linear accel/speed using the given informaiton.