Question

The coefficient of static friction between an ant and a gramophone disk is μs. The disk is rotating with constant angular velocity ω.

(a) What is the maximum point from the centre of the disk at which the ant should be sitting without slipping from the disk.
(b) What is the magnitude of the force from the disk on the ant in part (a).
(c) Where should the ant move in order to experience half the force from part (a).

Answer 1

The maximum point from the center of the disk at which the ant should be sitting is equal to the radius of the disk multiplied by the coefficient of static friction. The magnitude of the force from the disk on the ant can be determined using the equation F = mω²r. To experience half the force, the ant should move towards the center of the disk by half the maximum distance. Let's find :-

Now,

When an object is on the verge of slipping, the maximum point from the center of the disk at which the ant should be sitting is equal to the radius of the disk multiplied by the coefficient of static friction:-

r = μs * R

where r is the maximum distance from the center of the disk and R is the radius of the disk.

The magnitude of the force from the disk on the ant in part (a) can be determined using the equation:

F = mω²r

where F is the force, m is the mass of the ant, ω is the angular velocity of the disk, and r is the distance from the center of the disk.

In order to experience half the force from part (a), the ant should move towards the center of the disk by a distance of:

r' = r/2