You tie a 0.0750kg rock to a string

Question

and swing it like a conical pendulum. The radius of the circle is 25.00cm. When you measure the time it takes the stone to make one orbit, you find its 1.45s.

How fast is the rock moving? Assume the rock moves with a constant speed.

What is the angle θ that the string makes with the horizontal?

Answer 1

velocity magnitude is simply the circumference of the orbit divided by the period of the orbit.

T_y = mg and T_x = mv²/r or 4mπ²r/(period)² where T is the tension of the rope. Usually one defines θ as the vertical angle, but defining the angle with respect to the horizontal keeps Tx component as Tcos(θ) and Ty as Tsin(θ).

Take the ratio of the components and T drops out and tan(θ) = a function of g, v or T, and r. which is solvable.