What is the Maximum Angular Velocity of a Ball in Horizontal Circular Motion?

AI Thread Summary
The discussion revolves around calculating the maximum angular velocity of a ball in horizontal circular motion, given its mass, string length, and maximum tension. The tension equation T = mg + mLω² is debated, with confusion about whether to use angular velocity (ω) or linear velocity (v). Participants clarify that the centripetal force equation, which is typically mrω² or mv²/r, is applicable in this scenario, but the tension must also account for the vertical component when the string is at an angle. The importance of distinguishing between horizontal and vertical circular motion is emphasized, as the provided equation is more relevant to vertical scenarios. Understanding these distinctions is crucial for solving the problem accurately.
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Homework Statement



A ball of mass 0.5 kg is attached to the end of a string of length 0.5 m. The ball rotates in a horizontal circular path about a vertical axis. The maximum tension on the string cannot exceed 324 N. What is the maximum possible angular velocity of the ball in rad/s ?

Homework Equations



mω2/r = tension on the string.




The Attempt at a Solution



I don't think the equation is correct. It should be v and not ω. However, what I wanted to do was to equate the centripetal force with the maximum force on the string. I got the answer as 18, which is not correct. I tried to use mg instead of m but that was wrong too.

The correct equation is T = mg + mLω2, but why?

Why can I not use the centripetal force equation here?
 
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The centripetal force is given by mrω^2 or mv^2/r.
If this ball is on a table in a horizontal circle the r = 0.5m.
If the string is being held in the hand then there will be an angle ∅ to the horizontal.
You will then need to resolve the tension in the string into a vertical component to balance the weight of the ball and a horizontal component to provide the resultant centripetal force.
Hope this helps
 
Are sure it is in a HORIZONTAL circle !
The equation you have given as correct is for a VERTICAL circle !
 

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