Baseball Science Fair Project: Center of Percussion

Problem

Learn how the sweet spot correlates with movement and vibration.

Materials

• 2’ long wooden plank (a 2”x4” plank works well)
• U bolt
• Drill
• Smooth rod along which the U bolt can slide (e.g., shower curtain rod)
• Rubber mallet
• Tape measure
• Baseball bat

Procedure

1. Drill a hole through one end of the 2”x4” plank large enough to insert the U bolt. Use the bolt to hang the 2x4 from the curtain rod.
2. Mark a spot exactly halfway along the length of the wood. Strike it with the mallet in the direction parallel to the curtain rod. How does the wood move in response? Note how far along the curtain rod it moves.
3. Strike the end of the 2x4 farthest from the U bolt with the mallet. Is the movement different from last time? Which way does it move? How far? Note how far along the rod it moves now (taking note of the direction as well).
4. Starting at the far end, strike the wood at different distances from the end, moving towards the center each time. Keep track of how far you are from the edge of the wood and by how much the wood moves along the rod after each strike. Is there a spot where the wood barely moves along the rod at all?
5. Grab the baseball bat in one hand (holding it roughly where you would normally hold it if you were up to bat) and let it hang towards the ground.
6. Have a friend use the mallet to strike the bat at different distances from the far end of the bat. Take note of how the bat moves in your hand, taking particular note of any sensation of vibration. How does the sensation change as you strike the bat at different spots? Is there a spot where the vibration is minimal? It may help to close your eyes and concentrate on the vibrations you feel.

Results

When the wood is struck at the center, it moves sideways along the curtain rod but doesn’t rotate. When struck at the far end, the center doesn’t move, but the wood pivots around it, sending the U bolt moving in a direction opposite the direction of the blow. At some point along the wood, about 2/3 of the way down from the top, there will be a spot where the wood does pivot but it doesn’t move along the curtain rod.

Likewise, on the bat there will be a spot where the vibrations are smallest, probably around 17 cm from the end.

Why?

Every object has a center of mass, a point where you could balance the object perfectly. For a wooden plank of uniform density, that point is right in the middle. When you apply a force to an object’s center of mass, it will—not too surprisingly—move in the direction of the force. Go ahead and try it with a pencil (or something similar) on a table.

When you push on a point away from the center of mass, the object will start to rotate (this type of force, applied at a point away from the center of mass, is also called a torque). Pushing at one end or another will cause the object to rotate only; it won’t move sideways. Pushing anywhere between the end of the object and its center of mass makes things a bit more complicated: the object moves sideways (physicists call this translational motion) and it rotates (rotational motion).

When you whacked the middle of the wood, you applied a force at its center of mass. The wood responded by moving in the same direction as the force. When you hit the wood at its far end, it tried to spin around its center of mass, and the U-bolt moved in the opposite direction.

There’s a third point along the wood called the center of percussion, located about 2/3 of the way down.  When you strike this point, the resulting translational and rotational motions at the U bolt cancel. The U bolt tries to move forward and rotate backwards at the same time, but the two speeds are the same.

If you were holding that end when, say, a baseball struck right at that point, you would feel minimal kickback in the “bat”.

You probably noticed this when you tried the experiment with the bat and the mallet. You might feel the bat getting jerked either forward or backward in your hand, but when the strike occurred near the center of percussion, the bat barely moved at all.

Holding the bat also reveals something else: vibrations in the bat. When the bat is struck, standing waves travel along its length. These waves are stationary and cause the bat to bend ever so slightly. You can make standing waves with a Slinky or rope by holding both ends (better yet, get someone else to hold one end while you hold the other). Wiggle one end at just the right frequency, and the middle of the rope won’t move at all while the two halves move up and down in opposite directions from each other. Something similar happens in the bat. If you hit it at just the right spot, your hand will be at one of the points along the wave that doesn’t move (called a node). Getting a baseball to hit right at the sweet spot minimizes vibrations, takes some of the sting out of your hands, and sends the ball flying off with maximum speed.