Circular motion (A-level only) Flashcards – AQA A-level Physics (7408)

What is the formula for an angle $\theta$ in radians in terms of its arc length $s$ and radius $r$?

$\theta = \frac{s}{r}$

What is one radian?

The angle subtended at the centre by an arc whose length equals the radius.

How many radians are in one complete revolution?

$2\pi$ radians, equivalent to $360^\circ$.

What is angular speed?

The rate of change of angular displacement.

What is the unit of angular speed?

Radians per second.

For circular motion, how is angular speed $\omega$ related to speed $v$ and radius $r$?

$\omega = \frac{v}{r}$

How is angular speed $\omega$ related to the frequency of revolution $f$?

$\omega = 2\pi f$

How many radians correspond to one revolution?

$2\pi$ radians.

Why does an object moving in a circle at constant speed accelerate?

Its velocity continuously changes direction.

In what direction does centripetal acceleration act?

Towards the centre of the circle.

What is the magnitude of centripetal acceleration in terms of speed $v$, radius $r$ and angular speed $\omega$?

$a = \frac{v^2}{r} = \omega^2r$

What is centripetal force?

The resultant force directed towards the centre of a circular path, producing centripetal acceleration.

What is the magnitude of the centripetal force on an object of mass $m$ moving at speed $v$ in a circle of radius $r$?

$F = ma = \frac{mv^2}{r} = m\omega^2r$ Here $a$ is centripetal acceleration and $\omega$ is angular speed.

Should centripetal force be added as a separate force when accounting for the forces on an object?

No. Centripetal force is the role of the inward resultant force, not an additional force.