An astronaut's training centrifuge has a radius of 4.0m. If it goes round once every 2.5s, calculate the velocity of the end of the centrifuge arm (4.0m from the pivot).

Answer: 10.048m/s

Explanation:

We know that the radius is r = 4.0m

And for rotating things, the tangential velocity (or the velocity of the end of the centrifuge arm) can be calculated as:

v = r*w

The period is T = 2.5s,

This means that if sin (w*t) describes this situation, we have that:

sin (w*t) = sin (w * (t + T))

and we know that:

sin (w*0) = 0

sin (w * (0 + T)) = Sin (w*T) = 0

this means that w*T = 2*pi

w = 2*pi/T = 2*pi/2.5s = (2*3.14) / 2.5 s = 2.512 hz

Then the velocity can be calculated as

v = r*w = 4.0m*2.512hz = 10.048m/s