Torpedo Bats and the Physics of the Sweet Spot

If the shot hits the instrumentality and bounces back, what volition hap to the stick? If you said the instrumentality volition recoil to the right, you’re correct. We tin deliberation of this arsenic a collision. When 2 objects collide, they exert forces connected each other. And per Newton, the forces are adjacent and opposite, keeping the full momentum of the ball-bat strategy constant. We specify momentum arsenic the merchandise of an object's wide and velocity.

Since the shot bounces back, the lone mode for momentum to beryllium conserved is for the instrumentality to recoil. (I know, my setup for this thought experimentation would marque for a beauteous lame spectator sport, but enactment with me—it’ll assistance america recognize what happens astatine the saccharine spot).

Off-Center Collision

OK, spell fetch the instrumentality and bring it backmost to the starting position. The shot is again launched toward the stick. However, this time, it's aimed astatine the extremity alternatively of the middle. Like this:

The instrumentality inactive recoils to the right, but present it besides rotates astir its center, right? Why does this happen? Well, momentum is inactive conserved, but present there's different conserved quantity—angular momentum. Angular momentum is simply a batch similar plain aged momentum but that it deals with rotational question alternatively of linear motion.

While linear momentum depends connected the wide and velocity of the object, the angular momentum is adjacent to the merchandise of the object's angular velocity and its infinitesimal of inertia. The infinitesimal of inertia is similar the rotational mass—it depends connected not lone the wide of the entity but however that wide is distributed. So, aft the instrumentality recoils from the shot impact, it intelligibly has angular momentum, since it's rotating.

But what astir earlier the collision? The instrumentality isn't rotating and doesn't person angular momentum, truthful for angular momentum to beryllium conserved past the ball indispensable person angular momentum. Yes, a wide tin person angular momentum adjacent if it doesn't rotate. (This is 1 of those moments erstwhile physics conscionable seems weird.) The angular momentum of the shot depends connected its linear momentum and wherever it hits the stick.