Moderate -0.5 This is a dimensional analysis problem requiring students to equate dimensions of energy [ML²T⁻²] with the given expression. While it involves Further Maths Mechanics content (rotational kinetic energy), the method is straightforward and algorithmic: write dimensions, form equations, solve simultaneously. It's easier than average A-level questions because it requires no physical insight or problem-solving—just systematic application of a standard technique.
A disc, of mass \(m\) and radius \(r\), rotates about an axis through its centre, perpendicular to the plane face of the disc.
The angular speed of the disc is \(\omega\).
A possible model for the kinetic energy \(E\) of the disc is
$$E = km^ar^b\omega^c$$
where \(a\), \(b\) and \(c\) are constants and \(k\) is a dimensionless constant.
Find the values of \(a\), \(b\) and \(c\).
[3 marks]
A disc, of mass $m$ and radius $r$, rotates about an axis through its centre, perpendicular to the plane face of the disc.
The angular speed of the disc is $\omega$.
A possible model for the kinetic energy $E$ of the disc is
$$E = km^ar^b\omega^c$$
where $a$, $b$ and $c$ are constants and $k$ is a dimensionless constant.
Find the values of $a$, $b$ and $c$.
[3 marks]
\hfill \mbox{\textit{SPS SPS FM Mechanics 2021 Q1 [3]}}