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
