Question

A horizontal vinyl record of mass 0.10 kg and radius 0.10 m rotates freely about a vertical axis through its center with an angular speed of 4.7 rad/s and a moment of inertia of 5.0 × 10−4 kg m2 . Putty of mass 0.020 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

Answer:

The angular speed of the record is 3.36 rad/s.

Explanation:

Given that,

Mass of record= 0.10 kg

Radius = 0.10 m

Angular speed = 4.7 rad/s

Moment of inertia $I=5.0\times10^{-4}\ kgm^2$

Mass of putty = 0.020 kg

We need to calculate the angular speed

Using law of conservation of momentum

$L_{i}=L_{f}$

$I\omega_{i}=(I+mr^2)\omega_{f}$

$\omega_{f}=\dfrac{I\omega_{i}}{(I+mr^2)}$

Put the value into the formula

$\omega_{f}=\dfrac{5.0\times10^{-4}\times4.7}{5.0\times10^{-4}+0.020\times(0.10)^2}$

$\omega_{f}=3.36\ rad/s$

Hence, The angular speed of the record is 3.36 rad/s.