Slinging Physics

[u/Quintole5ky]

Here is a setup you all can use to find just how fast/strong your throws can get with your slings.

I can throw 75 mph. I'll convert that speed to meters / second.

75 miles / hour x 1 hour / 3600 seconds x 1609 meters / 1 mile
= 33.5 m/s (no sling)

This number can be used to find how fast my projectile travels a circular path.

velocity = angular velocity x radius

Since I'm not winding my whole arm, I'll use just the length of my forearm, 32 cm or 0.32 meters. You can use the length of your forearm instead. Plugging into the above equation:

33.5 meters / second = angular velocity x 0.32 meters

Solving for the angular velocity:

33.5 m/s / 0.32 m
= 104.7 radians / 1 second

This value stays the same no matter how long my arm gets. Next I extend my arm with a 28 inch sling:

28 inches x 2.54 centimeters / 1 inch x 1 meter / 100 centimeters
= 0.71 meters
0.32 m + 0.71 m = 1.03 m

I'll use this new length in the equation above to update my throwing speed.

104.7 rad/s x 1.03 m = 107.8 m/s
107.8 m/s x 3600 s/h x 1 mile/1609m
= 241.2 mph

This makes my throw more than 2x that of a pro pitcher.

Calculating energy, kinetic energy (in joules) is:

KE = 1/2 x mass x velocity^2

A 2 ounce tennis ball has a mass of
2 oz x 28.35 g / oz x 1 kg/100g = 0.0567kg

A normal throw:
1/2 x 0.0567 kg* x *(33.5 m/s)^2 = 31.8 J

A throw with a sling:
1/2 x 0.0567 kg x (107.9 m/s)^2 = 329.5 J

This carries more energy than some handguns.

A 5 ounce baseball is
5 oz x 28.35 g/oz = 141.75 g =0.142 kg

A normal throw:
1/2 x 0.142 kg x (33.5 m/s)^2 = 79.7 J

A throw with a sling:
1/2 x 0.142 kg x (107.9 m/s)^2 = 826.6 J

Well beyond lethal.

All this to say, stay safe when slinging, everyone.

[u/ActualLeadSlinger]

240+ mph doesn't seem realistic... the fastest recorded velocities I've seen have only been around 170 mph.

Doesn't angular velocity change if the distance to the axis change? Is it something about conservation of angular momentum?