norwich.typepad.com
The main idea of the slap shot is to convert the angular velocity of the rotation of a player's torso and stick to linear velocity of the puck leaving the stick. You can calculate the final velocity of the puck if you treat the situation like a collision problem and conservation of momentum. To determine the final velocity you need to find the momentum before the collision, calculate what it is after the collision and set them equal to each other since momentum is conserved. First you can start out with the equation for angular momentum, L=Iω, where L is the angular momentum, I is the moment of inertia, and ω is angular velocity. The moment of inertia from a player making a slap shot can depend on various things like body mass, length of stick, hand positioning on the stick, mass of the stick etc. Since there are many variables, finding a moment of inertia of a player can be quite complicated so we will assume I is constant. There is also a moment of inertia for the puck so we need to find that. The moment of inertia from the puck is a lot easier to find because it is small and uniform. We will treat it as a mass m at a distance r from the point of rotation, so it just ends up being mr². With these values you can come up with an equation for conservation of angular momentum while performing a slap shot:
ω1=Angular
velocity
of
player initial
ω2=Angular
velocity
of
player final
ω3=Angular
velocity
of
puck final
The puck does not go in a circular path when it is released from the
stick but
you can relate ω3 to
linear velocity with the equation rω3=V3
If the stick does not break during the slap shot then kinetic energy is
also
conserved. The kinetic energy of the rotating player is ½Iω²
and
the kinetic energy of the puck is ½mv². With these
values we can make a
second equation:
If we combine the two above equations we will get one equation where we can find the pucks final velocity.
ω3=2I*ω1
I+mr²
From
the equation above you can
notice two things. One is that puck's speed is related to the rotating
velocity
of the hockey player who is taking the slap shot. The second thing that
you can
notice is that the larger I the faster the shot will go,
technique in performing
the slap shot greatly affects the value of I.