Question

A horizontal vinyl record of mass 0.123 kg and radius 0.0958 m rotates freely about a vertical axis through its center with an angular speed of 4.82 rad/s and a rotational inertia of 2.19 x 10-4 kg·m2. Putty of mass 0.0400 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

The angular speed of the record is 1.8
`(rad)/(s)`

Step-by-step explanation:

Given:

Mass
`m = 0.123` kg

Radius
`r = 0.0958` m

Angular speed
`\omega _(i) = 4.82 (rad)/(s)`

Moment of inertia
`I = 2.19 * 10^(-4 )`
`Kg. m^(2)`

Mass of putty
`M = 0.0400` Kg

For finding the final angular speed,

According to the conservation of angular momentum,

`L_(i) = L_(f)`

`(I \omega _(i) ) = (I + Mr^(2) ) \omega _(f)`

`\omega _(f) = (I \omega _(i) )/(I + Mr^(2) )`

`\omega _(f) = (2.19 * 10^(-4) * 4.82 )/(2.19 * 10^(-4) + 0.040 * (0.0958) ^(2) )`

`\omega _(f) = 1.8 (rad)/(s)`

Therefore, the angular speed of the record is 1.8
`(rad)/(s)`