Rotational Motion Question 99
Question:A disc of mass (M) and radius (R) is rotating with an angular velocity $(\omega)$. If the radius of the disc is doubled keeping the mass same, what will be the new angular velocity?
Options:
A) $\omega$
B) $\frac{\omega}{2}$
C) $\frac{\omega}{4}$
D) $2\omega$
Show Answer
Answer:
Correct Answer: C
Solution:
The moment of inertia $(I)$ of a disc about its axis is given by $(\frac{1}{2}MR^2)$.
According to the conservation of angular momentum $(L = I\omega = \text{constant})$, if the radius is doubled, the new moment of inertia $(I’)$ becomes $(\frac{1}{2}M\left(2R\right)^2 = 2MR^2)$.
Therefore, the new angular velocity $(\omega’)$ must be such that $(I’\omega’ = I\omega)$.
Therefore, $2MR^2\omega’ = \frac{1}{2}MR^2\omega$.
Solving for $(\omega’)$, we get $(\omega’ = \frac{\omega}{4})$.
