Circular motion- how slowly would you twirl the ball in vertical circle

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SUMMARY

The discussion focuses on determining the critical speed required for an 800-gram ball to complete a vertical circle with a radius of 1 meter. The key equation used is v = √(gR), where g represents the acceleration due to gravity (approximately 9.81 m/s²) and R is the radius of the circle. The calculated minimum speed is 3.13 m/s, which ensures that the tension in the cord is zero at the top of the circle, allowing gravity to provide the necessary centripetal force.

PREREQUISITES
  • Understanding of centripetal force and its relationship with gravity
  • Familiarity with the equation v = √(gR)
  • Basic knowledge of units of mass and speed
  • Concept of tension in a cord during circular motion
NEXT STEPS
  • Explore the implications of varying the radius on critical speed in circular motion
  • Learn about the effects of mass on tension and speed in vertical circular motion
  • Investigate the role of angular velocity in circular motion dynamics
  • Study real-world applications of circular motion principles in sports and engineering
USEFUL FOR

Students studying physics, educators teaching mechanics, and anyone interested in the principles of circular motion and dynamics.

dani123
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Homework Statement



If you twirl a ball attached to a cord in a vertical circle, there would be a critical speed at the top for which the tension in the cord is zero. This is because the force of gravity supplies all the centripetal force necessary to complete the circle. How slowly would you twirl an 800-g ball so that it would describe a vertical circle of radius 1 m?

Homework Equations



Because we are looking for the slowest speed that the ball can have in order to complete the circle Fg=Fc
And therefore, through rearranging equations found that v=√gR

The Attempt at a Solution



So from that manipulated equation found that v=3.13m/s

If anyone could just verify my answer, that would be greatly appreciated! Thank you so much for your help and time!
 
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