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# Barbell Tipping

**12/12/11**

In bodybuilding/strength training forums I regularly read this question "How much weight can I add to one side of a racked barbell before it tips over?" There are a lot of simplifying assumptions one can make to tackle this problem, and here is a general idea. Statics experts (of which I am not one) - please write in!

Let a racked barbell that weighs B lbs have its supports at x_{1} and x_{2}. Say there is m_{1} lbs at
x_{1} and m_{2} lbs at x_{2}. The center of mass of the unweighted barbell itself is at d/2, where d is the length of
the barbell.

Note that for a bar to not be tipping, it is not rotating about a support. Therefore the sum of the torque equals zero. Mathematically, for an arbitrary point X, this is

_{1}*g*(X-x

_{1})+m

_{2}*g*(X-x

_{2})

Note that if sum(torques) = 0, this implies that X = X_{cm} (center of mass), and

_{cm}= (m

_{1}x

_{1}+m

_{2}x

_{2})/(m

_{1}+m

_{2})

I've ignored the weight, B lbs, of the bar here. Adding that back in, we get

_{cm}= (B*d/2 + m

_{1}x

_{1}+m

_{2}x

_{2})/(B+m

_{1}+m

_{2})

So when will the barbell tip over? Without loss of generality, assume we are just adding weight to m_{1}. The
bar will then tip when X_{cm} < x_{1}. That is, when the center of mass is outside of the support. The situation is:

Note something interesting here. Because each weight plate has a thickness, the new x_{1} point that we are loading with mass
is actually shifting to a number smaller than x_{1} as we add additional weight to the bar. So we're not just adding more weight,
but adding more weight further from the support.

If I substitute in specific numbers, these tend to match reality pretty well. For around 3 to 3+ plates it tends to tip for the setups I've used
if there are no plates on the other side (ie. m_{2} = 0). Here's a setup with some hypothetical numbers:

- B = 45 lbs
- bar's center of mass = d/2 = 42 inches
- starting m
_{1}= 45 lbs - m
_{2}= 0 lbs - starting x
_{1}= 24 inches - x
_{2}= 60 inches - assume x
_{1}shifts 3 inches to the left of the starting x_{1}with each plate added

Note that for 1 and 2 plates added to m_{1}, X_{cm} is still greater than 24 inches (the original x_{1}).
However, when a little over 3 plates are added, X_{cm} < 24, and therefore tipping occurs.

In practice, however, I'd recommend to not ever have the difference between m_{1} and m_{2} be large at all. Actually, there's really no need to use a barbell in the first place.

**Standard exercise disclaimer**: The material contained in this article is provided for informational purposes only. Before undertaking any form of exercise, you should consult with your physician. You should be aware if you engage in exercise you are doing so entirely at your own risk, including any present and/or future physical or psychological pain or injury that you may incur. The author of this content cannot assume any responsibility or liability for any injuries or losses that you may incur as a result of acting upon any information provided by this content, or any links to other exercise information found herein.

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