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

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In summary, the conversation discusses a physics problem involving a ball rotating about a vertical axis and the calculation of the angle at which the string should be cut so that it passes through the center of the circle. The solution involves using the conservation of energy to find the speed at an arbitrary angle, and then using the equations for projectile motion to determine the initial velocity components. The individual is advised to attempt the problem and use relevant formulas.
  • #1
fauxbeast
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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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  • #2
oh yea the speed of the ball is not constant. ie faster at the botton than the top.
 
  • #3
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
 

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

1. How do you calculate the angle θ in a rotating ball at point P?

To calculate the angle θ in a rotating ball at point P, you can use the formula θ = ωt, where ω is the angular velocity of the ball and t is the time elapsed. This will give you the angle in radians. Alternatively, you can use the formula θ = (v*t)/r, where v is the linear velocity of the ball and r is the radius of the ball's circular motion. This will give you the angle in degrees.

2. What factors affect the value of θ in a rotating ball at point P?

The value of θ in a rotating ball at point P is affected by the angular velocity, linear velocity, and radius of the ball's circular motion. Additionally, any external forces acting on the ball, such as friction or air resistance, can also affect the angle θ.

3. How does energy play a role in calculating θ in a rotating ball at point P?

Energy plays a crucial role in calculating θ in a rotating ball at point P. The energy of the ball can be represented by its kinetic energy, which is directly related to its angular velocity and linear velocity. The formula for kinetic energy is KE = 1/2 * I * ω^2, where I is the moment of inertia of the ball. As the ball rotates and its kinetic energy changes, the angle θ will also change.

4. What other factors should be considered when calculating θ in a rotating ball at point P?

In addition to the ball's angular velocity, linear velocity, and energy, it is also important to consider the direction of rotation of the ball. The angle θ will have a different value depending on whether the ball is rotating clockwise or counterclockwise. Additionally, if the ball is in contact with another surface, the properties of that surface, such as its friction coefficient, can also affect the value of θ.

5. Can the angle θ in a rotating ball at point P ever be negative?

Yes, the angle θ in a rotating ball at point P can be negative. This typically occurs when the ball is rotating in a counterclockwise direction and the angle is measured in a clockwise direction. In this case, the negative angle indicates that the ball has rotated past its starting position. Negative angles can also occur if the ball is rotating in a clockwise direction and the angle is measured in a counterclockwise direction.

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