All work must be shown A 0.300 kg, 1.00 m long rod is at rest on an icy surface

Question

All work must be shown

A 0.300 kg, 1.00 m long rod is at rest on an icy surface (no friction). Oddly enough, it has a 0.150 kg hockey puck glued to one end. A second hockey puck, also 0.150 kg, slides across the ice at speed 4.00 m/s perpendicular to the rod. As luck would have it, the sides of this second hockey puck are coated with sticky glue. The second puck hits the other end of the rod and sticks to it. The combination of stick and two pucks is then observed to slide across the ice while also rotating. What are the final speed, upsilon, and angular velocity, omega of the combination of stick and two pucks? The upper diagram shows the situation before the collision The lower diagram shows the situation immediately after the collision and at three later points in time.

Explanation / Answer

m = mass of puck

v = velocity of puck before collision

M = mass of stick

V = velocity of puck stick combination after collision

using conservation of linear momentum

mv = (M + 2m) V

V = mv/(M + 2m)                 

inserting the values

V = (0.15) (4) /(0.3 + 2 (0.15))

V = 1

L = length of stick

using conservation of angular momentum

mv(L/2) = (ML2/12 + m(L/2)2 + m (L/2)2) w

mv(L/2) = (ML2/12 + m L2/2) w

mv = (M/6 + m) (Lw)

(0.15) (4) = (0.3/6 + 0.15) (1) w

w = 3 rad/s

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