A (0.100-mathrm{kg}) ball attached to a (0.20-mathrm{m}) rod of very small inertia moves in a vertical circle

Question:

A \(0.100-\mathrm{kg}\) ball attached to a \(0.20-\mathrm{m}\) rod of very small inertia moves in a vertical circle in such a way that its speed remains constant. Let \(\mathcal{T}_{1}, \mathcal{T}_{2}, \mathcal{T}_{3}\), and \(\mathcal{T}_{4}\) be the tensions in the rod at positions 1, 2, 3, and 4 in Figure P11.34.

(a) Rank the tensions in order of magnitude, greatest first.

(b) What rotational speed is required at position 3 to keep \(\mathcal{T}_{3}\) barely greater than zero?

(c) At that speed, what is the tension at position 1 ?

Data from Figure P11.34