Question

A horizontal vinyl record of mass 0.0664 kg and radius 0.0714 m rotates freely about a vertical axis through its center with an angular speed of 4.31 rad/s and a rotational inertia of 6.86 x 10-4 kg·m2. Putty of mass 0.0475 kg drops vertically onto the record from above and sticks to the edge of the record.What is the angular speed of the record immediately afterwards

Answer 1

Here we can use Angular momentum conservation to resolve this question,

We can equal the Angular momentum of the vinyl record (circular disc) when it is moving freely and after sticking putty on the edge of the  vinyl record.

For that Initial Moment of inertial of the  vinyl record (I1), Initial angular velocity (ω1) was given on the question. Before trying to find the angular velocity after sticking putty on the edge of the  vinyl record (ω2) , we have to find the Moment of inertia after sticking putty on the edge of the  vinyl record (I2).

I2 =  I1 + mr^2                             (mr^2 = Moment of inertia of putty)

  = 6.86 x 10^-4 + 0.0475 x (0.0714^2)

  = 9.28x 10^-4

Then by,

I1 x ω1 = I2 x ω2

ω2     = (I1 x ω1 )/I2

          = (6.86 x 10^-4 x 4.31)/9.28x 10^-4

          = 3.19 rad/s