A2 June 2022 Q4

EdexcelCurrent spec8 marksHorizontal Circular Motion

4.

Figure 2: B vertically above A with AB = 6a; the string runs from B down to the ring R, at angle theta to the vertical, and from R horizontally back to A; R moves with angular speed omega on a horizontal circle with centre A
Figure 2

A small smooth ring \(R\) of mass \(m\) is threaded onto a light inextensible string. One end of the string is attached to a fixed point \(A\) and the other end of the string is attached to the fixed point \(B\) such that \(B\) is vertically above \(A\) and \(AB = 6a\)

The ring moves with constant angular speed \(\omega\) in a horizontal circle with centre \(A\). The string is taut and \(BR\) makes a constant angle \(\theta\) with the downward vertical, as shown in Figure 2.

The ring is modelled as a particle.

Given that \(\tan\theta = \dfrac{8}{15}\)

(a) find, in terms of \(m\) and \(g\), the magnitude of the tension in the string, (3)
(b) find \(\omega\) in terms of \(a\) and \(g\) (5)
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