Rotating pool table, calculating max ang. velocity

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SUMMARY

The discussion centers on calculating the maximum angular velocity for rotating a pool table without causing the balls to move. The user assumes a coefficient of static friction of 0.3 and dimensions of 50 inches by 100 inches, leading to a maximum angular velocity of approximately 9.7 RPM. A key point raised is the necessity of considering rolling friction, which differs from static friction, as it influences the balls' movement on the table. The calculation primarily relies on radial acceleration and the gravitational force, with static friction only relevant for determining the onset of skidding.

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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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