Advanced Higher Physics

Mandatory Course Key Areas - Aug 2018

Knowledge that an unbalanced torque causes a change in the angular (rotational) motion of an object.

Definition of moment of inertia of an object as a measure of its resistance to angular acceleration about a given axis.

Knowledge that moment of inertia depends on mass and the distribution of mass about a given axis of rotation.

Use of an appropriate relationship to calculate the moment of inertia for a point mass.

I={\mathrm{mr}}^2

Use of an appropriate relationship to calculate the moment of inertia for discrete masses.

I={\mathrm{\Sigma mr}}^2

Use of appropriate relationships to calculate the moment of inertia for rods, discs, and spheres about given axes.

rod about centre I=\frac{1}{12}{\mathrm{ml}}^2

rod about end I=\frac{1}{3}{\mathrm{ml}}^2

disc about centre I=\frac{1}{2}\mathrm{mr}

sphere about centre I=\frac{2}{5}{\mathrm{mr}}^2

Use of appropriate relationships to carry out calculations involving torque, perpendicular force, distance from the axis, angular acceleration, and moment of inertia.

$$\begin{gathered} \tau =\mathrm{Fr} \\ \tau =\mathrm{I\alpha } \end{gathered}$$

Use of appropriate relationships to carry out calculations involving angular momentum, angular velocity, moment of inertia, tangential velocity, mass, and its distance from the axis.

$$\begin{gathered} L=\mathrm{mvr}={\mathrm{mr}}^2\omega \\ L=\mathrm{I\omega } \end{gathered}$$

Statement of the principle of conservation of angular momentum.

Use of the principle of conservation of angular momentum to solve problems.

Use of appropriate relationships to carry out calculations involving potential energy, rotational kinetic energy, translational kinetic energy, angular velocity, linear velocity, moment of inertia, and mass.

$$\begin{gathered} E_{\mathrm{k(rotational)}}=\frac{1}{2}{\mathrm{I\omega }}^2 \\ {E}_p=E_{\mathrm{k(translational)}}+E_{\mathrm{k(rotational)}} \end{gathered}$$