Answer to Question #174439 in Classical Mechanics for Rohan

Question

A disk rotates with a constant angular velocity about its axis with respect to an inertial frame. There is a coaxial circular groove in the disk. A particle moves in the groove with a speed v as seen from the disk frame. At a certain instant a sharp blow increases the speed of particle from v to 2v. With respect to the disk frame, just after the blow the centrifugal force

(a) remains unchanged

(b) increases

(c) decreases

(d) is zero in both cases

Answer 1

Let the mass of the circular disk be M and radius be R,

Then Moment of inertia of the disk = $\frac{MR^2}{2}$

Angular momentum of the disk$=I\omega=\frac{MR^2}{2}\omega$

velocity of the particle in the groove is v

So initial angular momentum = $mr\times v$

here r is the radius of the groove

but after the external effort, velocity of the particle in the groove becomes 2v

So new angular momentum of the particle in the groove = $mr\times 2v$

So here the angular momentum of the system gets increase. because of the increase in the velocity of the particle which will lead to the increase in the centrifugal force.

Hence, correct answer will be option (b)