Answer to Question #122409 in Physics for jacob

Question

A horizontal vinyl record of mass 0.0592 kg and radius 0.144 m rotates freely about a vertical axis through its center with an angular speed of 4.39 rad/s and a rotational inertia of 6.41 x 10-4 kg·m2. Putty of mass 0.0468 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

Given, Before putting the Putty of mass $m=0.0468kg$ is $\omega_1=4.39rad/s$ ,Moment of inertia of Vinyl is $I=6.41\times 10^{-4}kg\cdot m^2$ .

Radius of horizontal Vinyl is $r=0.144m$ .

Now, After putting the Putty on Vinyl we have Moment of inertia is

$$I_2=I+mr^2=16.11\times 10^{-4} \: kg\cdot m^2$$

Now, As no external torque is acting thus Angular momentum is conserved,hence,

$$I\omega_1=I_2\omega$$

Hence,

$$\omega=\frac{I}{I_2}\omega_1\implies \omega\approx1.75rad/s$$

Thus, required angular velocity is $1.75rad/s$