Find the period of the conical pendulum given the angle (mass and string uniform circular motion).

In this mass and string uniform circular motion problem, we are given the angle of a conical pendulum relative to the vertical, and we solve for the period of rotation.

The conical pendulum is a simple plumb bob attached to a string that rotates in uniform circular motion with the string hanging below the horizontal. To analyze the uniform circular motion of the bob, we start with a force diagram including the weight vector pointing down and the tension in the string pulling up at an angle.

Next, we apply Newton's Second Law in the x and y directions to set up a system of equations in terms of the unknown tension and the period of rotation.

Finally, we solve the system to find the period of the conical pendulum, and we're done!

Bonus: explanation of how to get the formula for centripetal acceleration in terms of period.

[Reetdawn]

Cool vid, the little derivation of Ac was nice and informative😃