Standard +0.3 This is a straightforward application of conservation of angular momentum to two rotating bodies. Students need to recognize the principle, set up the equation I₁ω₁ + I₂ω₂ = I₁ω₁' + I₂ω₂', and solve for the unknown moment of inertia. While moments of inertia is a Further Maths topic (making it inherently harder), this particular question requires only direct substitution into a standard formula with no conceptual complications or multi-step reasoning.
1 Two flywheels \(F\) and \(G\) are rotating freely, about the same axis and in the same direction, with angular speeds \(21 \mathrm { rad } \mathrm { s } ^ { - 1 }\) and \(36 \mathrm { rad } \mathrm { s } ^ { - 1 }\) respectively. The flywheels come into contact briefly, and immediately afterwards the angular speeds of \(F\) and \(G\) are \(28 \mathrm { rad } \mathrm { s } ^ { - 1 }\) and \(34 \mathrm { rad } \mathrm { s } ^ { - 1 }\), respectively, in the same direction. Given that the moment of inertia of \(F\) about the axis is \(1.5 \mathrm {~kg} \mathrm {~m} ^ { 2 }\), find the moment of inertia of \(G\) about the axis.
1 Two flywheels $F$ and $G$ are rotating freely, about the same axis and in the same direction, with angular speeds $21 \mathrm { rad } \mathrm { s } ^ { - 1 }$ and $36 \mathrm { rad } \mathrm { s } ^ { - 1 }$ respectively. The flywheels come into contact briefly, and immediately afterwards the angular speeds of $F$ and $G$ are $28 \mathrm { rad } \mathrm { s } ^ { - 1 }$ and $34 \mathrm { rad } \mathrm { s } ^ { - 1 }$, respectively, in the same direction. Given that the moment of inertia of $F$ about the axis is $1.5 \mathrm {~kg} \mathrm {~m} ^ { 2 }$, find the moment of inertia of $G$ about the axis.
\hfill \mbox{\textit{OCR M4 2008 Q1 [4]}}