4. Monica stands at the edge of a circular platform that is slowly rotating on a frictionless axle. She then walks toward the opposite edge, passing through the platform’s center. Describe the motion of the platform as Monica makes her trip.

Explanation:

Since it is a circular platform, then Monica will move with an angular velocity from one edge of the platform to another while covering a specific radius.

Let's analyse her movement:

When Monica was initially at the edge of the platform, her angular velocity is at the lowest. Once she starts moving towards the centre of the circular platform, her angular velocity increases until she reaches the centre of the platform where the angular velocity will be at the maximum. The angular velocity is always at maximum when the radius is zero. At the centre of the platform the radius is zero making her angular velocity to be at maximum. As she moves toward the other end of the path from the center, her radius will increase and this increase in the radius will cause a decrease in her angular velocity.

This statement true according to the relationship between the angular velocity and the radius

w = v/r where

w is the angular velocity

r is the radius

It can be seen that the angular velocity is inversely proportional to the radius which means as the radius increases the angular velocity of Monica decreases and vice versa.

3. dark matter

empty space could also be a simple vacuum