Question

Two balls, each of mass m, are mounted on light rods which, initially, rotate in a horizontal plane with angular speed w about a fixed axis, as shown. An internal mechanism lowers the rods from the horizontal position to a position where the rods make an angle b with the horizontal, without interfering with the free rotation about the vertical axis. What is the new rate of rotation w'?

Answer 1

The new rate of rotation (w') is equal to the initial rate of rotation (w).

Step-by-step explanation:

The new rate of rotation (w') can be determined by applying the conservation of angular momentum. When the rods are lowered, the moment of inertia increases due to the redistribution of mass. Angular momentum is given by the equation:

L = Iw

Where L is the angular momentum, I is the moment of inertia, and w is the angular velocity.

Since angular momentum is conserved, we can equate the initial and final angular momenta:

Iw = I'w'

Where I' is the final moment of inertia, and w' is the final angular velocity.

However, since only the rods are lowered and the balls remain at the same distance from the axis, the moment of inertia does not change. Therefore, the new rate of rotation (w') is equal to the initial rate of rotation (w). So, w' = w.