Conical pendulumsAQA A-Level Further Maths: Mind map

Exam questions on Conical pendulums

1. A particle of mass $0.4$ kg is attached to a fixed point $O$ by a light inextensible string of length $0.8$ m. The particle moves in a horizontal circle below $O$ with constant speed, with the string taut and making an angle of $30^\circ$ with the downward vertical. Take $g=9.8$ m s⁻².
   Find the angular speed of the particle.2 marks
2. A particle of mass $0.6$ kg is attached to a fixed point $O$ by a light inextensible string of length $0.5$ m. It moves in a horizontal circle below $O$, with the string taut and making an angle $\theta$ with the downward vertical, where $\cos\theta=0.8$. Take $g=9.8$ m s⁻².
   Find the time taken for one complete revolution.2 marks
3. A particle of mass $m$ kg is attached to a fixed point $O$ by a light inextensible string of length $L$ m. It moves in a horizontal circle below $O$ with constant angular speed $\omega$ rad s⁻¹, with the string taut and making an angle $\theta$ with the downward vertical. Take $g=9.8$ m s⁻².
   Show that $\cos\theta=\frac{g}{\omega^2L}$.3 marks