CAIE A-Level Further Math AS 3.3.3 Circular Acceleration Questions

Practise analysing tension, angular speed and forces in horizontal circular motion with Further Mathematics Paper 2 questions and mark schemes.

Exam points

Apply de Moivre's theorem to powers and roots of complex numbers.

[Maximum number: 4]

One end of a light inextensible string of length a is attached to a fixed point O. The other end of the string is attached to a particle of mass m. The string is taut and makes an angle $\theta$ with the downward vertical through O, where $\cos \theta=\frac{2}{3}$ . The particle moves in a horizontal circle with speed v.

Find v in terms of a and g.

$\uparrow T \cos \theta=m g$ $\rightarrow T \sin \theta=\frac{m v^{2}}{a \sin \theta}$
Eliminate T and substitute for $\theta$ $v=\sqrt{\frac{5}{6} a g}$
4

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CAIE A-Level Further Math AS 3.3.3 Circular Acceleration Questions question 1