Two skaters of equal mass grab hands and spin

[Calpalned]

Homework Statement

On an ice rink two skaters of equal mass grab hands and spin in a mutual circle once every 2.5s. If we assume their arms are each 0.80m long and their individual masses are 55.0kg , how hard are they pulling on one another?

Homework Equations

## a_c = \frac {v^2}{R} ##
## v = \frac {D}{T} ##
## D = 2 \pi R ##

The Attempt at a Solution

With R = 0.8, and m = 55kg, I plugged it into ##F = m a = m \frac {v^2}{R} ## and I got the right answer. However, I don't understand why I have to use m = 55kg, rather than 110 kg (as there are two people spinning).

 

[haruspex]

Homework Statement

On an ice rink two skaters of equal mass grab hands and spin in a mutual circle once every 2.5s. If we assume their arms are each 0.80m long and their individual masses are 55.0kg , how hard are they pulling on one another?

Homework Equations

## a_c = \frac {v^2}{R} ##
## v = \frac {D}{T} ##
## D = 2 \pi R ##

The Attempt at a Solution

With R = 0.8, and m = 55kg, I plugged it into ##F = m a = m \frac {v^2}{R} ## and I got the right answer. However, I don't understand why I have to use m = 55kg, rather than 110 kg (as there are two people spinning).

Because the force acts on each. Each applies a force ##m \frac {v^2}{R} ## to the other, where m is the mass of one.