Rotating pool table, calculating max ang. velocity

[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!

 

[Meir Achuz]

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.

 

[charng]

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!