Calculating Angle θ in Rotating Ball at Point P - Energy + Other Stuff

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SUMMARY

The discussion focuses on calculating the angle θ at which a string should be cut to allow a rotating ball to pass through the center of its circular path. The ball, tied to a string and rotating vertically, has a speed at the top given by v = (gr)^0.5. Participants emphasize using conservation of energy to determine the speed at any angle and express the initial velocity components in terms of θ after the string is cut, transitioning the ball into projectile motion.

PREREQUISITES
  • Understanding of circular motion dynamics
  • Knowledge of conservation of energy principles
  • Familiarity with projectile motion equations
  • Ability to manipulate trigonometric functions for angle calculations
NEXT STEPS
  • Study the principles of conservation of mechanical energy in circular motion
  • Learn how to derive projectile motion equations from initial velocity components
  • Explore the relationship between angle and trajectory in projectile motion
  • Practice solving problems involving rotating bodies and energy conservation
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Students studying physics, particularly those focusing on mechanics, as well as educators seeking to enhance their understanding of circular motion and projectile dynamics.

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Homework Statement



As shown below, a ball is tied to one end of a string and the other end is fixed at point P. The ball is rotating about a vertical and at the top of its path has a speed v= (gr)^0.5 (don't know how to make a square root sign). At what angle θ should the sting be cut so that is passes through the center of the circle

https://mail.google.com/mail/?ui=2&ik=3fce58663c&view=att&th=12bebfdb82278d47&attid=0.1&disp=inline&zw


This is my first post, if i haven't correctly followed protocol please inform me. thanks in advanced for all the help.
 

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oh yea the speed of the ball is not constant. ie faster at the botton than the top.
 
You need to show some attempt to solve the problem.

This is a circular motion in a vertical plane at start. You know the speed at the top. Use conservation of energy to find the speed at an arbitrary angle.

After the string has been cut, the ball is a projectile. Express the vertical and horizontal components of the initial velocity in terms of the angle. Use the equation between the horizontal and vertical coordinates of the projectile so as it goes through the centre.

So collect the relevant formulas. Try to use them.

ehild
 

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