How Does a Conical Pendulum Maintain Constant Velocity?

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A conical pendulum consists of a mass suspended from a string that revolves in a horizontal circle, maintaining constant speed due to the balance of forces acting on it. The speed of the object can be expressed as v = √(L g sin(θ) tan(θ)), where L is the string length, g is the acceleration due to gravity, and θ is the angle of the string with the vertical. Key forces include tension and gravity, which together create the centripetal force necessary for circular motion. Understanding the momentum vector at any point in the circle is crucial for analyzing the system. The discussion emphasizes the need for initial effort and conceptual understanding to solve related problems effectively.
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A small object of mass(m) is suspended from a string of length (L). The object revolves with constant speed (v) in a horizontal circle of radius (r),(Because the sring sweeps out the surface of a cone, the system is known as a conical pendulum).Find that the expression for V (speed) is :

v= square root of (L g sin(theta) tan (theta)
 
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What are the forces acting on the object? What is the momentum vector of the object at any point in the circle?
 
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