Rotating pool table, calculating max ang. velocity

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To calculate the maximum angular velocity for a rotating pool table without the balls moving, a coefficient of static friction of 0.3 is assumed, with table dimensions of 50 inches by 100 inches. The calculated angular velocity is approximately 9.7 RPM based on the formula for radial acceleration. However, it's noted that this calculation only applies to flat objects and does not account for rolling friction. Rolling friction must be considered to prevent the balls from rolling, and it can be assessed by lifting the table until the balls begin to move. Accurate calculations require a comprehensive understanding of both static and rolling friction dynamics.
osumecheng
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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!
 
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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.
 

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