# Circular motion?

## Homework Statement

a test tube rotates in a centrifuge with a period of 1.2x10^-3s. The bottom of the test tube travels in a circular path of radius .15 m. with the centripetal force on a 2.00x10^-8kg amoeba at the bottom of the tube.

## The Attempt at a Solution

ac=v^2/r=(4pi^2r)/T
cross multiplied and got.
v^2x(1.2x10^-3)=4pi^2x(1.5^2)
divided
and solved for velocity and I got.
V=27.21

then fc=(m2v^2)/r
fc=(2x10^-8)x(27.210^2)/.15
fc=9.87x10^5????
supposed to be 8.22x10^2

THanks.

## Answers and Replies

Doc Al
Mentor
ac=v^2/r=(4pi^2r)/T
cross multiplied and got.
v^2x(1.2x10^-3)=4pi^2x(1.5^2)
divided
and solved for velocity and I got.
V=27.21
Two problems:
(1) That equation is not quite right. The right hand side should be: (4pi^2r)/(T^2)
(2) Why did you solve for V? What you want is v^2/r, which is given directly by the (corrected) right hand side.

It's not clear what the question is asking.

If you're looking for the force then you could start by finding the linear velocity. Just think distance divided by time and the circumference of the circle that the end of the tube is moving along.

You have a formula for the acceleration in terms of v and r. Compare this to Newton's second law and you should be able to get the accelerating (centripetal) force in terms of v and r as well.

LowlyPion
Homework Helper

## Homework Statement

a test tube rotates in a centrifuge with a period of 1.2x10^-3s. The bottom of the test tube travels in a circular path of radius .15 m. with the centripetal force on a 2.00x10^-8kg amoeba at the bottom of the tube.

## The Attempt at a Solution

ac=v^2/r=(4pi^2r)/T
cross multiplied and got.
v^2x(1.2x10^-3)=4pi^2x(1.5^2)
divided
and solved for velocity and I got.
V=27.21

then fc=(m2v^2)/r
fc=(2x10^-8)x(27.210^2)/.15
fc=9.87x10^5????
supposed to be 8.22x10^2

THanks.

Or more directly for the same result

F = m*ω2*r

where ω = 2π/T

F = m*(2π/T)2*r

Edit: I think the correct answer should have a (-) exponent ?

Last edited:
Two problems:
(1) That equation is not quite right. The right hand side should be: (4pi^2r)/(T^2)
(2) Why did you solve for V? What you want is v^2/r, which is given directly by the (corrected) right hand side.
Thanks
You are correct, The T^2 was my mistake. I have the right answer now (8.22 x 10^-2)

I do not understand what you mean by just using the right side?
ac=(4pi^2r)/T
there's no v there.
I solved for v to use the formula fc = (m2v^2)/r

Doc Al
Mentor
Thanks
You are correct, The T^2 was my mistake. I have the right answer now (8.22 x 10^-2)
I didn't check your calculation. Was it just a typo?

I do not understand what you mean by just using the right side?
ac=(4pi^2r)/T
there's no v there.
I solved for v to use the formula fc = (m2v^2)/r
You started with the equation: ac=v^2/r=(4pi^2r)/T^2
What you need (to move to the next step) is v^2/r, which equals (4pi^2r)/T^2. You don't need to know V explicitly:
ac=v^2/r=(4pi^2r)/T^2

thus:
Fc = mac = mv^2/r= m(4pi^2r)/T^2

You could go right to the answer using only r and T, which were given.

I didn't check your calculation. Was it just a typo?

You started with the equation: ac=v^2/r=(4pi^2r)/T^2
What you need (to move to the next step) is v^2/r, which equals (4pi^2r)/T^2. You don't need to know V explicitly:
ac=v^2/r=(4pi^2r)/T^2

thus:
Fc = mac = mv^2/r= m(4pi^2r)/T^2

You could go right to the answer using only r and T, which were given.

Oh in the sense f=ma. that makes sense.
Thank you.