Mace Swinging Physics: Centripetal force!

You may wonder how you can deadlift 150kg but only swing a 10kg mace, to a veteran powerlifter a 10kg mace sound like nothing, but due to the dynamic nature of the swinging motion, the force exerted on the body by the mace far exceeds the weight of the mace alone, this is due to centripetal force! Depending on the specific mace, a 10kg mace could typically actually pull with a peak force of 34kg at the centre of its back swing!

Due to the nature of what the mace is (a mass and long lever arm, where the centre of mass is positioned a long distance from our contact point) and how we use them (by swinging them is arcs, or circular paths) centripetal force becomes very relevant!

Centripetal force is the force required to keep a mass moving on a circular path. Newtons first law states "an object in motion stays in motion with the same speed and same direction, unless acted upon by an external force". In our case, centripetal force is the external force which directs the motion of the mace into a circular path, as opposed to letting the mace fly off away from our body.

Unlike a barbell deadlift, for example, where you are only fighting the weight of the mass due to gravity, in the case of the mace, you are fighting both the weight of the mass but also the centripetal force required to keep the mace moving on its circular path. 

Let's dig into some analysis for the example of a 7kg vs 10kg mace; the magnitude of centripetal force required keep an object moving along its circular arc is dependent on: 

• The velocity of the object, v, in m/s, the higher the velocity, the more centripetal force required 
• The radius of motion between the centre of mass and the pivot point of the object, r, in m, the smaller/tighter the radius, the more centripetal force required 
• The mass of the object, m, in kg, the higher the mass, the more centripetal force required 

 These 3 factors are linked by the following formula to calculate centripetal force, in Newtons: 

We know that the mass remains constant and radius of motion during a mace swing, such as the 360 or 10-2, remain near enough constant, therefore from the above formula it is clear that the peak centripetal force will occur when the velocity of the mace is the highest, this happens during the centre of the back swing:

By analysing the motion of the mace frame by frame through the centre portion of the back swing, we can figure out the radius of motion and velocity of the mace. We do that by having a reference scale of known length, in this case the length of mace handle between the pommel and the head of the mace is 93cm, and by knowing the frame rate the video was shot in, in this case, 960FPS super slomo. 

So let's do that for our example of a 7kg mace: 

We now have all the factors required to calculate the centripetal for I am required to exert on the mace to keep it moving in its arc: 

Plus the weight of the mace itself means there is a total downward pull exerted by the mace of 23kg! A whole lot more than the 7kg weight of the mace when you take it at face value! 

 Let's repeat the process for a 10kg mace: 

Plus the weight of the mace itself, that means in the centre of the back swing, this 10kg mace is exerting a downward pull of 34kg! 11kg more than the 7kg mace despite only being 3kg heavier! 

This shows you how the mace can generate much more force than you may imagine by taking its weight at face value!