3 upvotes, 2 direct replies (showing 2)
View submission: Ask Anything Wednesday - Physics, Astronomy, Earth and Planetary Science
If we assume that you throw like a windmill, perfectly rotating your arm about a fixed point on your shoulder, then we can determine how the lever arm length affects the launch velocity. Let's call the lever arm length "R". Assuming you have the same rotational speed regardless of your lever arm then we can translate your rotational motion to linear via (omega)x(R) = V, where omega is that rotational rate and V is your launch velocity. So the impact on your lever arm length is linear to your launch velocity: **twice the lever arm results in twice the launch velocity**
Ignoring air resistance and assuming you always release at the same angle, we now need to know how your launch velocity affects your throw distance. Some re-arranging of kinematics equations eventually yields that for a initial velocity V and launch angle (theta), the distance of a throw is equal to: (V^2 )xsin(2xTheta)/(g) where g is the acceleration due to gravity. So that means that **twice the launch velocity results in four times the distance thrown**
Putting it all together your experiment seems correct! Ignoring air resistance and all other factors held constant, **Doubling a lever arm will result in a throw four times as far**
Comment by thehotbreadguy at 27/04/2023 at 04:35 UTC
3 upvotes, 0 direct replies
What a fantastic explanation! I won't pretend to understand much of it, but thank you for verifying my observations!
Comment by sunburn_on_the_brain at 27/04/2023 at 15:42 UTC
2 upvotes, 0 direct replies
I believe I read a while back that windmill designers can get something like 4x the energy generation if they double the length of the blades, so that would match up with what you have there.