The angular speed of a body changes from omeg | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Since no external torque is applied,the angular momentum of the body remains conserved.$L_1 = L_2$$I_1 \omega_1 = I_2 \omega_2$We know that the mo

Vedclass · Accepted Answer

$\sqrt{\omega_2} : \sqrt{\omega_1}$

Vedclass · Answer

(A) Since no external torque is applied,the angular momentum of the body remains conserved.$L_1 = L_2$$I_1 \omega_1 = I_2 \omega_2$We know that the moment of inertia $I$ can be expressed in terms of the radius of gyration $K$ as $I = MK^2$,where $M$ is the mass of the body.Substituting this into the conservation equation:$M K_1^2 \omega_1 = M K_2^2 \omega_2$$K_1^2 \omega_1 = K_2^2 \omega_2$Rearranging the terms to find the ratio of radii of gyration $K_1/K_2$:$\frac{K_1^2}{K_2^2} = \frac{\omega_2}{\omega_1}$Taking the square root on both sides:$\frac{K_1}{K_2} = \sqrt{\frac{\omega_2}{\omega_1}} = \sqrt{\omega_2} : \sqrt{\omega_1}$

The angular speed of a body changes from $\omega_1$ to $\omega_2$ without applying a torque but due to changes in moment of inertia. The ratio of radii of gyration in two cases is

Similar Questions

What does not change in the field of a central force?

Different minerals are being mined from within the earth and multi-storeyed complexes are being constructed. Due to this activity,theoretically:

If the earth suddenly shrinks to $\frac{1}{64}$th of its original volume with its mass remaining the same,the period of rotation of earth becomes $\frac{24}{x} \text{ h}$. The value of $x$ is $.......$

If the radius of the Earth were to suddenly decrease,then:

Vedclass Test Series

Exam Paper Generator

Online Exam Module