Two wheels P and Q are connected by a belt. Radius of P is three times radius of Q. If both wheels have the same rotational kinetic energy and I₁/I₂ = x:1, find x.

Question

G1 Physics · Accepted Answer

The belt does not slip, so rim speeds are equal: ω₁(3R)=ω₂R, hence ω₂=3ω₁. Equal rotational kinetic energies give ½I₁ω₁²=½I₂ω₂². Therefore I₁/I₂=(ω₂/ω₁)²=3²=9, so x=9.