A puck moves on a horizontal air table.It is attached to a string that passes through a hole in the center of the table.As the puck rotates about the hole,the string is pulled downward very slowly and shortens the radius of rotation,so the puck gradually spirals in towards the center.By what factor will the puck's angular speed have changed when the string's length has decreased to one-half of its original length?
A)2
B)4
C) $\sqrt { 2 }$
D)1
E)1/2

Question

Quizplus · Accepted Answer

The angular speed of the puck increases by a factor of 4 when the string's length is decreased to one-half of its original length. This is because angular momentum (L) is conserved in the absence of external torques, and L = Iω, where I is the moment of inertia and ω is the angular speed. For a point mass moving in a circle, I = mr^2, so L = mr^2ω. When the radius (r) is halved, the new moment of inertia is (1/4)mr^2, and to conserve angular momentum, the angular speed (ω) must increase by a factor of 4.

A Puck Moves on a Horizontal Air Table 2\sqrt { 2 }2​

A Puck Moves on a Horizontal Air Table $\sqrt { 2 }$