A object is being rotated in a if the acceleration of the centrifuge is 4g what is the velocity of the object and the time period of its motion

Question

An object is being rotated in a centrifuge of radius 4m if the acceleration of the centrifuge is 4g what is the velocity of the object and the time period of its motion. 

Answer 1

I believe f=ma leads to f=mv^2/r, which means a=v²/r, then v=sqrt(ar)=sqrt(4*4)=4m/s

 

Then v=distance/t, 4=2πr/t , so t=8π/4 = 2π 0r  6.28 seconds

Answer 2

Piyush,

Generally, a centrifuge runs at a set speed. Now since acceleration is defined as the change in velocity over time, we must realize that the acceleration of a centrifuge is not a change in the speed of rotation, but the change in the direction of travel, i.e. going in a circle. So the acceleration of a centrifuge is also known as centripetal force. The equation for that is:

ƒ = mv² / r

 

f = centripetal force

m = mass of the object

v = tangential velocity

r = radius of the circular path

 

Velocity is the desired number so we rework the equation to:

 

v = √(ƒr/m)

 

v = √(4*9.81*4/4) = 6.26 m/s

 

To find the period, we need the circumference:

 

C = 2*π*4 = 8π meters

 

time = distance / velocity = 8π / 6.26 = 4.01  or  4 seconds

 

I hope that helps.