Conical pendulum




3 forces acting on a conical pendulum

  • Gravity(=mg): The force the Earth pulls.
  • Tension: The force applied to both ends of the thread. Tension is always directed to the center from both ends.
  • Centripetal force(Fc): The force that maintains circular motion. The centripetal force always toward the center of rotation.

Conical pendulum

Fc=mrω2=mr(2πT)2

ω: Angular velocity of rotational motion (rad/s)
T: period of rotational motion (seconds)

Find the period of a conical pendulum

Consider a conical pendulum with a line length ‘L’ and a rotation radius ‘r.’
Centripetal force(Fc) is the result of gravity and tension. Also, the centripetal force is perpendicular to gravity. From this, the following equation is calculated.

Fc=mgtanθ

Substituting the definition of centripetal force comes the following equation.

mr(2πT)2=mgtanθ

(2πT)2=grtanθ

Since it is tanθ=rh, we can make it a bit simpler.

(2πT)2=gh

Solving the above equation for the period T, It becomes as follows.

T=2πhg

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