Consider the depicted conical pendulum: a mass m on the end of a string of length L, which is fixed to the ceiling. Given the proper push, this pendulum can swing with an angular velocity ω in a circle at an angle α with respect to the vertical, maintaining the same height throughout its motion. Different positions of the mass are indicated by North, West, South, East (N, W, S, E).

 

What is the net force on the mass when it is in the North position, expressed in terms of the sum of all forces acting on the mass? Use "g" for the gravitational acceleration, "a" for the angle ?, T for the tension on the string, and "o" for the angular velocity ?.

What is the net force on the mass when it is in the North position, expressed in terms of the centripetal force?

what is the tension on the cable in terms of the angle ??

What is the angular velocity squared in terms of the angle ??

If the mass is 5.4 kg, the angle 21 degrees, and the length of the cable 1.6 meters, what is the linear speed of the ball?

L mE S--