Slapshot

During Thanksgiving break, I was fortunate enough to attend an NHL hockey game between the Washington Capitals and the Edmonton Oilers. It was a rather uneventful game with very few opportunities coming from either side. However, in the third period, the Capitals finally broke the deadlock with an awesome 90 mph slapshot by Dimitry Orlov to the top right corner of the goal. Given the awesomeness of the goal I found myself wondering what angular acceleration was placed on Orlov's hockey stick to give the puck such great speed. Additionally I found myself wondering what the total kinetic energy was given to the puck because the shot gave it both translational and rotational kinetic energy. With all of this in mind:

http://www.real-world-physics-problems.com/physics-of-hockey.html

Final speed of puck: 90mph --> 40.2 m/s

Length of hockey stick (r) --> 1.8m

Let's say it takes .3 seconds to get a shot off

v = r ω

40.2 m/s = 1.8m ω

ω = 22.3 rad/s

α = Δω/Δt

α = (22.3rad/s - 0rad/s) / (.3s)

α = 74.4 rad/s²

Now Kinetic Energy:

v = 40.2m/s

w = 3rev/s

Approx puck moment of inertia as cylinder --> ½ mr²

r = 3.8 cm

m = 170g

KE total = KE trans + KE rot

KE = ½ mv² + ½ I ω²

KE = ½ mv² + ¼ m r²ω²

KE = ½ (.170kg) (40.2m/s)² + ¼ (.170kg) (.038m)² (2π*3rev/s)²

KE = 137.4 J