That's a very difficult question to answer, because you give us
no information regarding what you have done in your life.
We can only assume that you have most likely breathed on occasion,
floated on your back in the ocean, lake or pool, maybe fallen off of a
ladder or out of bed, felt the warmth of the sun on your cheek, seen
a rainbow after a rainshower, heard the sound of thunder during a
summer storm, taken a trip in an airplane, and waited for a cup of
hot chocolate to cool off. The richness of any of these experiences
is greatly enhanced when you understand some of the Physics involved.
Answer:
μsmín = 0.1
Explanation:
- There are three external forces acting on the riders, two in the vertical direction that oppose each other, the force due to gravity (which we call weight) and the friction force.
- This friction force has a maximum value, that can be written as follows:

where μs is the coefficient of static friction, and Fn is the normal force,
perpendicular to the wall and aiming to the center of rotation.
- This force is the only force acting in the horizontal direction, but, at the same time, is the force that keeps the riders rotating, which is the centripetal force.
- This force has the following general expression:

where ω is the angular velocity of the riders, and r the distance to the
center of rotation (the radius of the circle), and m the mass of the
riders.
Since Fc is actually Fn, we can replace the right side of (2) in (1), as
follows:

- When the riders are on the verge of sliding down, this force must be equal to the weight Fg, so we can write the following equation:

- (The coefficient of static friction is the minimum possible, due to any value less than it would cause the riders to slide down)
- Cancelling the masses on both sides of (4), we get:

- Prior to solve (5) we need to convert ω from rev/min to rad/sec, as follows:

- Replacing by the givens in (5), we can solve for μsmín, as follows:

Answer:
If one cup falls down then there will be 59 cups left.