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 system is equal to the final angular momentum of the system. 
Initial angular momentum = mr1^2ω1
Final angular momentum = mr2^2ω2
where m is the mass of the puck, r1 and r2 are the initial and final distances from the hole, and ω1 and ω2 are the initial and final angular velocities.
Plugging in the given values, we get:
Initial angular momentum = (0.005 kg)(2.0 m)^2(3.0 rad/s) = 0.06 kg m^2/s
Final angular momentum = (0.005 kg)(1.0 m)^2(ω2)
Setting the two equal and solving for ω2, we get:
0.06 kg m^2/s = (0.005 kg)(1.0 m)^2(ω2)
ω2 = 12 rad/s
Therefore, the new angular velocity is 12 rad/s, which is choice C.

A Puck on a Frictionless Air Hockey Table Has a Mass