A puck on a frictionless air hockey table has a mass of 5.0 g and is attached to a cord passing through a hole in the surface as in the figure.The puck is revolving at a distance 2.0 m from the hole with an angular velocity of 3.0 rad/s.The cord is then pulled from below,shortening the radius to 1.0 m.The new angular velocity (in rad/s)is
A)4.0
B)6.0
C)12
D)2.0
E)8.0

Question

A puck on a frictionless air hockey table has a mass of 5.0 g and is attached to a cord passing through a hole in the surface as in the figure.The puck is revolving at a distance 2.0 m from the hole with an angular velocity of 3.0 rad/s.The cord is then pulled from below,shortening the radius to 1.0 m.The new angular velocity (in rad/s)is 
A)4.0 
B)6.0 
C)12 
D)2.0 
E)8.0

Quizplus · Accepted Answer

The conservation of angular momentum states that the initial angular momentum of the puck must be equal to its final angular momentum.

Initial angular momentum = mvr (where m = mass, v = velocity, and r = radius)
Final angular momentum = mv'r' (where v' = final velocity and r' = final radius)

Setting these two equations equal to each other and solving for v', we get:

v' = (r/r') * v

Plugging in the values given in the problem, we get:

v' = (2/1) * 3.0 rad/s = 6.0 rad/s

Therefore, the new angular velocity is 6.0 rad/s, which corresponds to choice (C).

A Puck on a Frictionless Air Hockey Table Has a Mass