# Math Behind Shooting/Passing

Shooting and passing in lacrosse involves Sir Isaac Newton’s three laws of motion. The first law of motion is inertia which states that a body at rest will stay at rest until acted on by an external force. This can be seen in passing when the ball is in your stick. Unless you make a force giving energy to propel the ball forward, the ball will stay in your stick. Newton’s second law of motion gives us the Formula F=MA. In this formula, force, or the speed at which the ball leaves the stick is equal to the mass of the ball times the acceleration you put on it through your stick. This formula is also used for the speed of the stick which is directly attributed to the speed at which the ball will leave the stick. The force or speed at which your stick moves is dependent on the mass of the stick times the acceleration of the stick. Since the mass (weight) of a lacrosse ball is a constant 5 ounces, the speed at which the ball moves is almost completely dependent on the speed at which the stick moves. This means that a heavier stick, although taking more strength accelerated at the same speed as a lighter stick, will cause the ball to travel at a faster speed.

Although in principle accelerating the ball and stick sounds like an easy t ask, many people find controlling the stick to be a difficult task. This is because the stick acts as a lever, which needs to be pushed with the top hand and pulled with the bottom hand. This creates a fulcrum at the top hand. The formula for a lever is F=(W*X)/L. In this formula W is the total load weight, or the weight of the ball, X is the length to the fulcrum, and L is the length from the fulcrum. X is the length from the top hand to the head of the stick where the ball sits, L is the length from the top hand to the bottom hand, and as aforementioned, W is the weight of the ball.

Another important aspect of passing or shooting a lacrosse ball is the fact that the

farther the object is from its axis of rotation, the faster its linear speed will be. The formula for linear speed is V=S/T, where S is the distance traveled and T is the time taken. So combined with the speed the stick moves by using the lever formula, the distance from the axis which is the center of your body at which the stick moves has an effect on the speed of the ball. This is why in lacrosse, it is taught to get your hands as far away from your body as possible when shooting, so that the distance is increased and the speed of your shot will be faster.

The last aspect that goes into shooting or passing is that linear speed is great, but it must be transformed into rotational momentum in order to finally propel the ball forward. To turn linear speed into rotational momentum, a player must plant his foot and use friction. The formula for friction is where F(f) is the magnitude of friction, U is the coefficient of friction, and F(n) is the normal force exerted. The formula for normal force is where F(n) is normal force M is mass and G is gravity. This means that a heavier person will exert a greater normal force, thus creating a greater force of friction causing more of the linear speed to be transferred to rotational momentum. It has been found that top players can create a rotational momentum of over 1300 degrees per second.

Although shooting is a very important aspect of lacrosse, we have not yet taken into account the goalie and goal which in the end are the target when taking a shot. We will next examine the effects and math behind goaltending in lacrosse.

Works Cited:

• “Linear Speed Formula.” Linear Speed Formula. N.p., n.d. Web. 09 Mar. 2016.
• “Friction Formula.” Friction Formula. N.p., n.d. Web. 09 Mar. 2016.
• “Lever Mechanical Advantage Equation and Calculator – Case #1 | Engineers Edge | Www.engineersedge.com.” Lever Mechanical Advantage Equation and Calculator – Case #1 | Engineers Edge | Www.engineersedge.com. N.p., n.d. Web. 09 Mar. 2016.
• (Photo) Robert Goldstein
• “Newton’s Three Laws of Motion.” Newton’s Three Laws of Motion. N.p., n.d. Web. 09 Mar. 2016.
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