uniform circular motion

Vocabulary flashcards covering key definitions, concepts, and equations of circular motion from the lecture notes.

Radian

The angle subtended at the centre of a circle by an arc equal in length to the radius of the circle.

Degree to Radian Conversion

The process of converting an angle from degrees to radians by multiplying by $\frac{\pi}{180}$. For example, converting $8^\circ$ to radians gives $8 \times \frac{\pi}{180}$.

Angular Displacement

The change in angle, measured in radians, when a body rotates round a circle ($\Delta \theta$).

Angular Speed ($\omega$)

The rate of change of angular displacement with respect to time, given by $\omega = \frac{\theta}{t}$, $\omega = \frac{2\pi}{T}$, $\omega = 2\pi f$, or $\omega = \frac{v}{r}$.

Centripetal Force

The resultant force acting towards the centre of the circle to keep an object in uniform motion around the circle, given by $F = \frac{m v^2}{r}$ or $F = m \omega^2 r$.

Centripetal Acceleration

The acceleration directed towards the centre when an object moves around a circle at constant speed, given by $a = \frac{v^2}{r}$ or $a = r \omega^2$.

Uniform Circular Motion

Motion around a circular path where speed is constant because it is a scalar magnitude component, but velocity constantly changes because its direction constantly changes.

Radian

The angle subtended at the centre of a circle by an arc equal in length to the radius of the circle.

Degree to Radian Conversion

The process of converting an angle from degrees to radians by multiplying by $\frac{\pi}{180}$.

Angular Displacement

The change in angle, measured in radians, when a body rotates round a circle ($\Delta \theta = \theta_2 - \theta_1$).

Angular Speed ($\omega$)

The rate of change of angular displacement with respect to time.

Angular Speed Formulae

Equations representing angular speed: $\omega = \frac{\theta}{t}$, $\omega = \frac{2\pi}{T}$, $\omega = 2\pi f$, and $\omega = \frac{v}{r}$.

Centripetal Force

The resultant force acting towards the centre of the circle to keep uniform motion around a circle.

Centripetal Force Formulae

Equations used to calculate centripetal force: $F = \frac{m v^2}{r}$ and $F = m \omega^2 r$.

Centripetal Acceleration

The acceleration towards the centre when an object moves around a circle at constant speed.

Centripetal Acceleration Formulae

Equations used to calculate centripetal acceleration: $a = \frac{v^2}{r}$ and $a = r \omega^2$.

Uniform Circular Motion

Motion around a circular path where speed is constant because speed is a scalar magnitude component, while velocity constantly changes because its direction constantly changes.