When two players collide on the field, they exert forces on each other. These forces are often much larger then all the other forces that are also acting on the players, but they only act for a very short time. If during that short time interval we only consider the forces the players exert on each other and neglect all other forces, we can predict the motion of the center of mass of each player just after the collision using only momentum conservation.
Newton's 2nd laws, when applied to an extended object, predicts the motion of a particular reference point for this object. This reference point is called the center of mass.
How do we find the center of mass (CM) of of an object?
Every extended object has a center of mass. If near the surface of Earth an object, in any orientation, is supported at a location directly below its center of mass or suspended from a location directly above its center of mass, it will be balanced and it will not start to rotate.
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Usually, but not always, the center of mass of an object lies within the object itself. For example, the center of mass of a ball is the very middle of the ball, and the center of mass of a book is the middle of the book.
How about the center of mass of a person?
In most men, the center of mass is located at or slightly above the navel, in most women it is located below the navel, closer to the hips.
If an object has parts that can move with respect to each other, the location of the center of mass depends on the positions of the parts. For example, when a cheerleader lifts her arms, her center of mass moves to a higher position in her body than when her arms are at her side.
How does the CM of a player move just after a collision?
When two players collide, then the net force on each player during the collision is nearly equal to the force exerted on him by the other player. The center of mass of the player accelerates in the direction of this force, a = F/m, the velocity of the CM changes. But as soon as the collision is over, the interaction force vanishes, and the subsequent acceleration is due to the sum of all the other forces acting on the player. If this sum is small, then the velocity of the CM of the player stays nearly constant.
Let us study the motion of some players after a one-on-one collision, and let us compare this motion with the motion of the carts that we studied in the collision lab.
Step through the examples below!
When studying the video clips of collisions on the field, it becomes immediately clear that the motion of the two players after a collision is much more complicated than the motion of the carts. The motions of the CMs of the players and the carts immediately after the collision is similar, but the carts subsequently move with nearly constant velocity, while the players slow down quickly or fall down. There are two main reasons for this difference in motion.
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During the collisions not only the velocity, but also the angular velocity of a player changes. Often the player has zero angular velocity before the collision and non-zero angular velocity after the collision. |
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The net force acting on a player after the collision can also produce a torque and therefore change the angular velocity of a player. |
Why does it get so complicated?
Players are extended objects, not mass points. Extended object can have translational and rotational motion. Any motion of an extended object can be viewed as a combination of translational motion of the center of mass and rotational motion about the center of mass.
Example:
The sponge toss: A foam square has a blue LED near its CM and a red LED near its edge. If we toss the sponge we can easily observe the parabolic motion of the CM and the rotational motion about the CM.
