Question

Young softball batters are often instructed to “choke-up on the bat” by their coach. In terms of the moment of inertia, what exactly does this accomplish and why is it an advantage to the young batter? Come up with one other real-life example where either increasing or decreasing the moment of inertia becomes an advantage? Clearly describe the example and talk about the variables involved.

Answer 1

When a person bats they’re (usually) seeking to maximize the force of contact between the ball and the bat through efficient use of their body. Since the person is swinging, the action is akin to pulling a lever. That is, something is (approximately) rotating about a point or axis. There are a lot of variables that go into this, but roughly the force of contact is related to a torque created by the motion of the arms and bat (as well as a portion of the torso). The strength of this force partly depends on the distance, r, the contact point is from the axis of rotation. Take a look at the picture below.

So the torque at the point of contact, independent of the action of the ball itself, is where is the moment of inertia for the bat/arm combination. Roughly, we can approximate it as a cylinder pivoting around one of its endpoints. This is not a perfect analogy, but it will work for the argument here.is the angular velocity of the bat/arm combination, i.e. how fast the batter swings the bat. So the torque can be determined without even considering the ball. However, the contact itself also creates a torque since torque also happens to be . Note this is a cross product. That means only the components of the force and vector, r, that are orthogonal (perpendicular) to one another multiply.

many batters actually ‘choke down‘ on the bat to get more power. Specifically, the very bottom of the bat is gripped by either the middle or ring finger of their lower hand, leaving one or two fingers gripping at air. Then, right around the time of contact (ideally at the time of contact), they flick their wrists a bit (the grip simply makes this action a bit easier). This applies a secondary torque since, briefly, the bat is also pivoting around its base (in addition to the bat/arm combination pivoting around the axis along the body). Since torques and forces are additive, this increases the force of contact slightly. It’s a nifty little trick of physics – if you can get the timing right. Get it wrong and you’re likely to pull the ball foul.

Now we could also look at all of this from the standpoint of momentum. In the above case, the momentum of both the swing and the flick of the wrist is associated with some angular motion and is thus called angular momentum. Nonetheless, a linear momentum is associated with this at the point of contactand, like forces and torques (and, indeed, all vectors) momentum is additive. This helps explain one more trick batters often use. Frequently batters will, just before their swing, pick their leading foot up and step forward a bit as they swing. This effectively transmits a small amount of linear momentum to the entire body and thus to the contact as well. This gets added to the other two pieces of momentum and, if perfectly executed, is the recipe for a great hit.

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