Question

A thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of the disc. The insect now moves along a diameter of the disc to reach its other end. During the journey of the insect, the angular speed of the disc.
a) Continuously increases
b) Continuously decreases
c) first increases and first decreases
d) remains unchanged

Answer 1

Hint: No external torque is applied on the system. A system's angular momentum is conserved as long as there is zero net external torque working on the system. The angular momentum is presented by the moment of inertia, i.e., how much mass of the object is in motion and how distance it is away from the centre, multiplies with the angular velocity.

Complete answer:
external torque will be zero on the system.
Apply conservation of angular momentum-
$I_{1} \times w_{1}$ = $I_{2} \times w_{2}$
I is a moment of inertia.
w is angular speed.
So, we get
$ I \times w$ = constant
The insect is moving from the edge to the centre of the circle and then from centre to edge of the disc.
Moment of inertia and angular speed are inversely proportional to each other.
$w \propto \dfrac{1}{I}$
Moment of inertia is directly proportional to r, where r is the distance from the centre.
First insects move from edge to centre, r will decrease. So, I will also decrease.
As moment of inertia and angular speed are inversely proportional, so w will increase.
After reaching the centre, the insect will move from centre to edge of the circular disc.
r will increase. So, I will also increase.
As moment of inertia and angular speed are inversely proportional, so w will decrease.

Option C is correct.

Additional Information:
If an external force is zero on a body, then the momentum will remain constant, and if the force cannot cause a body to move, the body remains at rest, and the body's momentum remains zero.

Note:
Angular momentum's conservation is similar to the conservation of linear momentum. Angular momentum is a vector quantity whose conservation states the reason that a rotating system proceeds to rotate at the constant motion unless a torque is applied to it.