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 must be equal to the final angular momentum.

Linitial = Lfinal

Li = Iωi  (where I is moment of inertia, ωi is initial angular velocity)
Lf = If ωf (where If is final moment of inertia, ωf is final angular velocity)

Since the mass of the puck and the radius changes, we can assume that moment of inertia has changed.

Initial moment of inertia (Ii) = mr^2 = 5.0 g x (2.0 m)^2 = 20 g m^2
Final moment of inertia (If) = mr^2 = 5.0 g x (1.0 m)^2 = 5.0 g m^2

Using the conservation of angular momentum, we can write:

Iiωi = Ifωf

(20 g m^2) (3.0 rad/s) = (5.0 g m^2) (ωf)

ωf = (20 g m^2 / 5.0 g m^2) (3.0 rad/s)

ωf = 12 rad/s

Therefore, the new angular velocity is 12 rad/s, which corresponds to choice (C).

A Puck on a Frictionless Air Hockey Table Has a Mass