# Rotating pool table, calculating max ang. velocity

• osumecheng
In summary, a pool table with a constant angular velocity would need to rotate at approximately 9.7 rpm to prevent the balls from moving. However, this calculation does not take into account rolling friction, which would affect the movement of the balls. The coefficient of static friction is not relevant in this calculation. To accurately determine the required rotation speed, rolling friction must be considered by lifting the table until the balls start to roll.

#### osumecheng

Hi,
I am trying to calculate how fast you could rotate a pool table (at constant angular velocity) without the balls moving.
Assumptions used: coeffecient of static friction=0.3
table dimensions: 50in.X100in.
So the farthest distance from the center is 111.8 in.
I came up with about 9.7 rpm by setting radial acceleratio=R*omega=coeff. friction*g
Can anyone check me on this, not sure if I did it right. Thanks!

The balls would roll. Your calc would work only for a flat object.
You need to include "rolling friction" (Which is not really friction) to keep the balls from rolling. The coefficient of static friction does not enter your calculation, except to determine when the balls would start to skid.
Rolling friction can be determined by lifting the table until the balls start to roll.

Hello, it seems like you have approached the problem correctly. The maximum angular velocity of the rotating pool table would indeed be limited by the coefficient of static friction and the dimensions of the table. As you have correctly calculated, the maximum angular velocity would be approximately 9.7 rpm, which is equivalent to 1.02 radians per second. This means that the table can rotate at a constant speed of 1.02 radians per second without the balls moving. It is always important to double check your calculations and assumptions, but based on the information provided, your solution seems reasonable. Good job!

## 1. How does a rotating pool table work?

A rotating pool table is a specially designed pool table that can rotate around its central axis. This rotation allows players to experience a different type of gameplay, where the balls move in curved paths instead of straight lines.

## 2. What is the maximum angular velocity of a rotating pool table?

The maximum angular velocity of a rotating pool table depends on its size and the force applied to it. Generally, the larger the table and the greater the force applied, the higher the maximum angular velocity will be.

## 3. How is the maximum angular velocity of a rotating pool table calculated?

The maximum angular velocity of a rotating pool table can be calculated using the formula v = ωr, where v is the tangential velocity, ω is the angular velocity, and r is the radius of rotation.

## 4. Can the maximum angular velocity of a rotating pool table be changed?

Yes, the maximum angular velocity of a rotating pool table can be changed by adjusting the force applied to it. Increasing the force will result in a higher maximum angular velocity, while decreasing the force will result in a lower maximum angular velocity.

## 5. Are there any safety precautions to consider when playing on a rotating pool table?

Yes, players should always be cautious when playing on a rotating pool table. They should ensure that the table is stable and secure before playing, and should never stand on the table while it is rotating. It is also important to follow the rules and guidelines of the game to prevent accidents and injuries.