Fall is upon us, which means a brand new school year has started for millions of students around the globe. For that reason, I thought it would only be appropriate if we started this academic year off with another installment of Circus Science! This time we will take a look at a classic circus stunt, the Globe of Death. Grab your pencils, calculator and motorcycle helmet-it’s going to be a wild ride…

The Globe of Death traditionally involves several performers riding motorcycles around in circles on the inside of a metal globe. This feat is heavily based on timing between the riders to make sure they don’t crash into each other, but the reason they can ride around in circles and can ride upside down in the first place is a physics phenomenon called **centripetal force**. Centripetal force is the force that acts on an object as it moves around in a circular path. All forces have a direction in which they push, and centripetal force is directed towards the center of the circular path. In other words, if you are driving your car in a circle, the centripetal force is directed towards the center of that circle. Centripetal force can be calculated using the following equation:

Fc = (m x v2) / r

Where:

Fc is the centripetal force

m is the mass of the object

v is the velocity at which the object is moving

r is the radius of the circular path. The radius of a circle is the distance from the center of the circle to the outer edge. It is half the length of the diameter.

Now if you are traveling on a flat, horizontal surface, that’s all you need to calculate the centripetal force and there’s nothing more to it. However, things get a little bit more difficult when you start to add in an up-and-down vertical movement, as is the case with the Globe of Death. For that, we need to learn about two more forces.

The **force of gravity** pulls everything downward towards the ground. The force of gravity is *always* directed straight down. It doesn’t matter what position an object is in, the force of gravity will always be straight down. The force of gravity can be calculated using the following equation:

F_{g} = m x g

Where:

F_{g} is the force of gravity

m is the mass of the object

g is the acceleration due to gravity (an accepted constant on Earth)

The **normal force **is a little bit trickier than gravity. Every action has an equal and opposite reaction, but what exactly does this almost cliché statement *really* mean? Well think about it this way: Go outside and push the wall of any nearby building. Go ahead, I’ll wait. You’re back? Great. You should have noticed that the wall stayed standing (if it didn’t, please consult with your general contractor of choice). You exerted a force on the wall, and the wall exerted *the same force back on you*, hence the lack of movement. If the wall didn’t exert the same force back, it would fall over. Now back to the normal force. An object exerts a force on whatever surface it is on. It doesn’t matter if the object is on a slant or even upside down, in the case of the motorcycle and rider at the top of the Globe of Death. The surface then exerts a force back on the object, the normal force. If the object is on a flat, horizontal surface (it doesn’t matter if it is right side up or upside down), the normal force can be calculated using the following equation:

F_{N} = m x g

Where:

F_{N} is the normal force

m is the mass of the object

g is the acceleration due to gravity (an accepted constant on Earth)

When dealing with objects moving in circular paths that aren’t completely horizontal, the centripetal force is the sum of these two other forces. Consider the case of the motorcycle and rider when they are completely upside down at the top of the globe. At this exact moment, the centripetal force is equal to the force of gravity on the motorcycle and rider, plus the normal force exerted on the motorcycle and rider by the globe (F_{c} = F_{g} + F_{N}).

So at this point, you’re probably saying, “Okay Matthew. That’s all great. But why is this important? Who cares?” I get it, you want answers. This information is valuable because it can be used to determine the minimum velocity the rider and motorcycle must be moving so they don’t fall down as they go upside down.

The moment the motorcycle and rider slows enough that they start to fall and lose contact with the top of the globe, the normal force immediately goes down to zero. The motorcycle is not in contact with the globe, hence no force is being exerted on the globe, so the globe doesn’t have to exert anything back. We can plug zero in as the normal force into the general relationship we derived earlier (F_{c} = F_{g} + F_{N}) and work backwards to find the velocity.

F_{c} = F_{g} + F_{N}

F_{c} = F_{g} + 0

F_{c} = F_{g}

(m x v^{2}) / r = m x g

(m x v^{2}) = m x g x r

v^{2} = (m x g x r) / m

v^{2} = g x r

v = (g x r)^{1/2}

^{ }

As the above derivation shows us, the velocity at which the motorcycle and the rider fall off the top of the globe is the square root of the acceleration due to gravity multiplied by the radius of the globe; anything faster than this velocity and the motorcycle and rider will be able to complete the path successfully. Additionally, because the acceleration due to gravity is constant on Earth, the **only **thing that influences how fast to ride is the size of the globe. Bigger globe, faster ride. Simple as that. The size of the motorcycle, the weight of the rider, they don’t matter. It’s just the size of the globe, which brings us to the close of our first lesson of the new school year! Until next time… SCIENCE!

*Matthew “Phineas” Lish, 19, is an award-winning clown and juggler. Notable performances include off-Broadway, the Ronald McDonald House, the Century Club with Dick Cavett, and guest ringmaster at the Big Apple Circus. He will be joining the world famous Ringling Bros. and Barnum & Bailey Clown Alley in January 2017, and currently holds the world record for juggling clubs while bouncing on a pogo stick. *

Mr. Stadler is very proud of you 😉 Good luck in January!