A light circular platform can rotate freely about its central vertical axis

PHYSICS · Multi-part · A Level · Physics · Engineering physics · Engineering physics

Problem

OO'

. Three small blocks

P

Q

and

R

of masses

0.40\,\text{kg}

0.50\,\text{kg}

and

m\,\text{kg}

respectively are placed on the platform at perpendicular distances

0.15\,\text{m}

0.25\,\text{m}

and

x\,\text{m}

from the axis. When the platform is tested, its moment of inertia about

OO'

is found to be exactly

0.070\,\text{kg m}^{2}

. (i) Derive an equation connecting

m

and

x

that satisfies the given moment of inertia. (ii) If the manufacturer decides to keep

m = 0.30\,\text{kg}

, calculate the corresponding value of

x

. (iii) For the same total mass of the three blocks, explain whether keeping

x

larger or smaller makes the platform easier to start rotating, giving a brief justification.