# Centrifugal carrot

By Marcus Wilson 23/02/2010 1

We bought a vegetable juicer recently.   At one end you feed in all those delicious carrots and corguettes that have been growing nicely in the vegetable patch, and at the other end comes out carrot and corguette juice.  Get the right combination of vegetables, and it’s a nice drink. (I don’t recommend kohlrabi though. Actually, we haven’t found anything nice to do with our kohlrabi other than adding it straight to the compost bin – the trouble is we planted rather a lot of it – if anyone has any tips they would be greatly appreciated)

Our juicer is a ‘centrifugal’ type.  That means the veggies get ripped apart first of all by a rotating blade with little piranha-teeth on it, then the bits get thrown against a mesh where the centrifugal force squashes the juice out of the veggie-piece. The juice flows through the mesh and then is collected, whereas the bits make their way to the top of the revolving bit (which is wider at the top than the bottom) and are then thrown out and collected elsewhere.   Very efficient, and very viscious.   The warning about not inserting your fingers into the machine is there for good reason.

I’m not sure just how fast the centrifuge bit rotates, but it is certainly beyond the ability for the eye to ‘see’ the movement – everything just blurs into one. So I would say it is at least 20 times a second, possibly a lot more.   It has a radius of about 5 cm or so.   A little bit of physics calculation tells me the centripetal acceleration of a lump of carrot at the centrifuge rim – namely 4 times pi squared times rotation rate squared times radius.  (The acceleration is equal to the angular rotation rate squared times the radius.)   So we’d have 4 times 3.14 squared times (20 per second) squared times 0.05 metres which comes to about 800 metres per second squared.

Compare this with the acceleration due to gravity  of about 10 metres per second squared.   The veggie-lump experiences about 80 times this. I suspect this is a conservative estimate.  So it gets squashed very nicely.

N.B.  No apologies made for referring to ‘centrifugal’.  See  http://sci.waikato.ac.nz/physicsstop/2008/12/going-around-in-circles.shtml and the xkcd cartoon below.

### One Response to “Centrifugal carrot”

• Aimee Whitcroft says:

hahaha! that’s one of my favourite xkcd strips ever – it adorned the walls of my beige cubicle for ages when i was working in the consultancy biz…