CAIE A-Level Further Mathematics 3.3.3 Horizontal Circular Motion

Practise resolving tension or normal reaction vertically and radially for uniform horizontal circles, then relating radius, angular speed and period.

Exam points

resolve vertically for equilibrium and radially for acceleration towards the circle's centre
express the circular radius from the string or surface geometry before using angular speed
convert angular speed to period only after the force equations have fixed its exact value

[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.

$\uparrow T \cos \theta=m g$

B1

$\rightarrow T \sin \theta=\frac{m v^{2}}{a \sin \theta}$

B1

Eliminate T and substitute for $\theta$

M1

$v=\sqrt{\frac{5}{6} a g}$

A1

4

All question bank results loaded

3.3.3—Circular acceleration question 1