A.4.4 (HL)—Angular motion quantities

Three angular quantities

Angular displacement $\theta$ describes change in orientation, angular velocity $\omega=d\theta/dt$ describes how fast orientation changes, and angular acceleration $\alpha=d\omega/dt$ describes how angular velocity changes.

Link to linear motion

At radius $r$ , tangential speed is $v=r\omega$ . Keep angular quantities in radians when using these relationships.

Common trap

Angular velocity is not automatically the same as linear speed; the radius is needed to connect them.

How it is assessed

The evidence asks for angular velocity of a point on a circle and time to reach a specified angular position.

Command terms

Calculate

What earns marks

Use ω=v/r for angular velocity and relate angular displacement, angular velocity and time with the stated motion. Convert revolutions to radians when a full-turn quantity is given.

Watch for

Using circumference or linear speed without dividing by radius, or mixing revolutions with radians.

Representative question

[Maximum number: 1]

Calculate the angular velocity $\omega$ of P.

$\omega=\frac{v}{r}=\frac{2}{0.9}=2.22 \mathrm{rads}^{-1}$

Torque and rotation

Use $au=Fr\sin heta$ , $\sum au=0$ for rotational equilibrium and $\sum au=Ilpha$ for angular acceleration. Always state the axis and use the matching moment of inertia.

Describe angular motion

Use angular displacement, angular velocity and angular acceleration; rotational SUVAT applies only for uniform $lpha$ . Point-mass inertia is $I=\sum mr^2$ .

Track angular momentum

$L=I\omega,\quad \Delta L= au\Delta t$

Conserve angular momentum only when external resultant torque is negligible.

Track rotational energy

$E_{rot}= rac12I\omega^2$

For rolling or coupled systems, include translational and rotational energy separately.

A.4.4 (HL)—Angular motion quantities

Describe Angular Motion

A.4.4 Exam Analysis

Assessment in practice

Retrieve the A.4 Rigid Body Mechanics Model

Question 1