Calculating time period in vertical circular motion

In summary, the conversation discusses how to calculate the minimum time period needed for a cone filled with water to complete a vertical circular motion without the water falling. The equations used involve the velocity and the application of the law of conservation of energy. The individual seeking help has found an equation for velocity but is unsure how to calculate the time needed for one revolution due to the varying velocity. A possible solution suggested is to research the Elliptic Integral of the First Kind.
  • #1
taninamdar
3
0
1. 1. Homework Statement :
How to calculate minimum time period 't' required to complete a vertical circular motion by a cone filled with water, so that the water doesn't fall?
2. Homework Equations :
v^2 = gR * [ 3 + 2 cos (theta) ] obtained by applying law of conservation of energy.


3. 3. The Attempt at a Solution :
I have found that v^2 = gR * (3 + 2 cos theta ). But the velocity varies with theta. So, how to calculate the time required to complete one revolution using variable velocity?


Thanks!
 
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  • #3
Hello Taninamdar,

Welcome to Physics Forums!

You might want to research "Elliptic Integral of the First Kind," perhaps. Good luck!
 

What is vertical circular motion?

Vertical circular motion is the motion of an object in a circular path that is perpendicular to the ground, where the object's speed and direction are constantly changing.

What is the time period in vertical circular motion?

The time period in vertical circular motion is the amount of time it takes for the object to complete one full revolution around the circular path.

How do you calculate the time period in vertical circular motion?

The time period in vertical circular motion can be calculated using the formula T = 2π√(r/g), where T is the time period, r is the radius of the circular path, and g is the acceleration due to gravity.

What is the relationship between the radius and time period in vertical circular motion?

The time period in vertical circular motion is directly proportional to the radius of the circular path. This means that as the radius increases, the time period also increases, and vice versa.

Can the time period in vertical circular motion be affected by other factors?

Yes, the time period in vertical circular motion can be affected by the object's mass, speed, and the strength of the gravitational force. These factors can change the acceleration due to gravity, which in turn affects the time period.

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