Question

A disc of mass 2 kg and radius 0.2m is rotating with velocity 30rad/s .What is angular velocity ,if a mass of 0.25kg is put on periphery of the disc?

Answer 1

Answer:

The angular velocity is 24 rad/s

Explanation:

Initial angular velocity of the disc

$\omega_1=30 rad/s$

Mass of the disc M = 2kg

Radius of the disc R = 0.2m

The moment of inertia of the disc

$I_1=\frac{1}{2}MR^2$

Mass of the object m = 0.25 kg

Moment of inertial of the system (disc and object)

$I_2=\frac{1}{2}MR^2+mR^2$

Since there is no external torque

Therefore, the angular momentum will be conserved

Thus,

$I_1\omega_1=I_2\omega_2$

$\implies \frac{1}{2}MR^2\times\omega_1=(\frac{1}{2}MR^2+mR^2)\times \omega_2$

$\implies \frac{M\omega_1}{2}=(\frac{M}{2}+m)\times \omega_2$

$\implies \frac{2\omega_1}{2}=(\frac{2}{2}+0.25)\times \omega_2$

$\implies 30=1.25\times \omega_2$

$\implies \omega_2=\frac{30}{1.25}$

$\implies \omega_2=24$ rad/s

Hope this helps.

Answer 2

Got that anwer ? Hope to understood It is a super easy question!