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

What is angular displacement, and in what unit is it measured?

The change in angular position of a rotating object, measured in radians.

What determines the sign of angular displacement?

The chosen positive direction of rotation.

How does angular speed differ from angular velocity?

Angular speed is a scalar rate of rotation; angular velocity also specifies the direction of rotation.

What is the average angular velocity over a time interval?

$\omega = \frac{\Delta\theta}{\Delta t}$

What is angular acceleration?

The rate of change of angular velocity.

What is the average angular acceleration over a time interval?

$\alpha = \frac{\Delta\omega}{\Delta t}$

How do instantaneous angular velocity and acceleration differ from their average values?

Instantaneous values are rates of change at a particular instant; average values are calculated over an interval.

What are the units of angular velocity and angular acceleration?

Angular velocity: $\mathrm{rad\,s^{-1}}$; angular acceleration: $\mathrm{rad\,s^{-2}}$.

What are the rotational counterparts of translational displacement, velocity and acceleration?

Angular displacement, angular velocity and angular acceleration, respectively.

What does the gradient of an angular displacement–time graph represent, and how is its instantaneous value found on a curve?

It represents angular velocity. On a curve, use the gradient of the tangent at the relevant time.

How can instantaneous angular acceleration be found from an angular velocity–time graph?

Find the gradient of the graph at the relevant time.

What does the signed area between an angular velocity–time graph and the time axis represent?

Angular displacement.

How do angular velocity–time graphs differ for uniform and non-uniform angular acceleration?

Uniform: a straight line with constant gradient. Non-uniform: a changing gradient.

What does the signed area between an angular acceleration–time graph and the time axis represent?

The change in angular velocity.

For constant angular acceleration, what equation relates final angular velocity $\omega_2$ to initial angular velocity $\omega_1$, angular acceleration $\alpha$ and time $t$?

$\omega_2 = \omega_1 + \alpha t$

For constant angular acceleration, what equation relates angular displacement $\theta$ to initial angular velocity $\omega_1$, final angular velocity $\omega_2$ and time $t$?

$\theta = \left(\frac{\omega_1 + \omega_2}{2}\right)t$

For constant angular acceleration, what equation relates angular displacement $\theta$ to initial angular velocity $\omega_1$, angular acceleration $\alpha$ and time $t$?

$\theta = \omega_1 t + \frac{\alpha t^2}{2}$

For constant angular acceleration, what equation relates final angular velocity $\omega_2$ to initial angular velocity $\omega_1$, angular acceleration $\alpha$ and angular displacement $\theta$ without using time?

$\omega_2^2 = \omega_1^2 + 2\alpha\theta$

Why is the mean angular velocity the average of the initial and final angular velocities when angular acceleration is constant?

Because angular velocity changes uniformly.

What sign convention is required when using the equations of uniformly accelerated angular motion?

Use a consistent positive direction for angular displacement, angular velocity and angular acceleration.

How do the equations of uniformly accelerated angular motion correspond to those for translational motion?

They have the same form, with angular displacement, velocity and acceleration replacing their translational counterparts.