Balancing Brooms - finding the centre of mass

05 May 2011


Balancing Brooms


Scrubbing the deck

Two hands forming a heart shape

A broom, mop, ruler, or something else long and straight2 hands


Point the index fingers of both hands and hold your hands apart but parrallel.

Get someone to balance the broom horizontally on your two index fingers, making sure you keep them level.

Now gently move your fingers together.


You should find that as long as you keep your fingers level the broom stays balanced, even as they get very close together.  You have found the broom's centre of gravity.


When you start off holding the broom inevitably one finger will be closer to the centre of mass than the other.

Broom centre of mass

This means that more of the weight will be sitting on the closer finger, so it must be pushing upwards harder.

Reaction forces on broom

The larger the force between the finger and the broom the larger the maximum frictional force it can provide before it slides.

Friction is larger near the centre of mass

The finger furthest from the centre of mass will therefore be able to slide the most easily, and it moves until it is no longer the furthest from the centre of mass. 

Other side of the broom moves

Then the other finger can move, so they keep sliding in such a way as they move closer and closer to the centre of mass and the broom stays balanced.


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