Conical Pendulum with free sliding ring

In summary, the problem involves a particle of mass m tied to a string of length 2L, with one end fixed to a vertical pole and the other end attached to a ring of mass m. The particle moves in a horizontal circle and the goal is to find the minimum angular velocity required for the particle to continue in this motion. To solve this, one must find the tension in each string by drawing free body diagrams and applying Newton's Second Law.
  • #1
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Homework Statement



A particle of mass m is tied to the middle of a light, inextensible string of length 2L. One end of the string is fixed to the top of a smooth vertical pole. The other end is attached to a ring of mass m, which is free to slide up and down the pole. The particle moves in a horizontal circle.
Find the least possible value of [tex]\omega[/tex] for the particle to continue in this motion.

Homework Equations



[tex]F_{centripetal} = m\omega ^2 r[/tex]

The Attempt at a Solution



I'm not really sure how to begin with this... I've tried visualising the situation in my head but I can't imagine what would happen in a frictionless situation and how the angular velocity would affect it

thanks
 

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  • #2
Begin by finding the tension in each string. To do this draw a free body diagram of the mass that is going around. Write Newton's 2nd law for that mass in the vertical and horizontal direction. You may not assume that the tension is the same in each string. Draw another free body diagram for the ring and write its Newton's Second Law equation. Put the the three equations together to get an expression for the angular speed.
 
  • #3
Just imagine that the particle moves along a horizontal circle and the ring stays at a certain height, and draw the free-body diagram for both the particle and the ring. The resultant force on the particle is equal to the centripetal force. The resultant force on the ring is equal to zero.

ehild
 
  • #4
Thanks :)
 

FAQ: Conical Pendulum with free sliding ring

What is a conical pendulum with a free sliding ring?

A conical pendulum with a free sliding ring is a type of pendulum in which the hanging object is attached to a ring that can slide freely along the length of the string. This allows the pendulum to swing in a conical motion rather than just back and forth.

How does a conical pendulum with a free sliding ring work?

The motion of a conical pendulum with a free sliding ring is governed by the forces of gravity and tension in the string. As the pendulum swings, the ring slides up or down the string, changing the angle at which the pendulum swings and causing it to move in a circular motion.

What factors affect the motion of a conical pendulum with a free sliding ring?

The motion of a conical pendulum with a free sliding ring is affected by the length of the string, the mass of the hanging object, and the angle at which the string is released. Other factors such as air resistance and friction can also impact the motion.

What is the purpose of a conical pendulum with a free sliding ring?

A conical pendulum with a free sliding ring is primarily used for educational purposes to demonstrate the principles of circular motion and the effects of changing variables on the motion of a pendulum. It can also be used in physics experiments to study the forces acting on the pendulum.

What are some real-life applications of a conical pendulum with a free sliding ring?

A conical pendulum with a free sliding ring has practical applications in various fields such as astronomy, navigation, and engineering. It can be used to determine the Earth's rotation and to measure the acceleration due to gravity. It is also used in gyroscopes and accelerometers to detect and measure motion and rotation.

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