DP Physics (last assessment 2024)

Question 19M.3.SL.TZ2.a

[Maximum mark: 2]

19M.3.SL.TZ2.a

The moment of inertia of a solid sphere is $I = \frac{2}{5}m{r^2}$ where m is the mass of the sphere and r is the radius.

Show that the total kinetic energy E_k of the sphere when it rolls, without slipping, at speed v is ${E_{\text{K}}} = \frac{7}{{10}}m{v^2}$ .

[2]

Markscheme

E_k = E_k linear + E_k rotational

${E_{\text{k}}} = \frac{1}{2}m{v^2} + \frac{1}{2}I{\omega ^2}$ ✔

$= \frac{1}{2}m{v^2} + \frac{1}{2} \times \frac{2}{5}m{r^2} \times {\left( {\frac{v}{r}} \right)^2}$ ✔

« $= \frac{7}{{10}}m{v^2}$ »

Answer is given in the question so check working is correct at each stage.

Examiners report

The derivation of the formula for the total kinetic energy of a rolling ball was well answered.

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