A circular flywheel of radius \(0.3\) m, with moment of inertia about its axis \(18\) kg m\(^2\), is rotating freely with angular speed \(6\) rad s\(^{-1}\). A tangential force of constant magnitude \(48\) N is applied to the rim of the flywheel, in order to slow the flywheel down. Find the time taken for the angular speed of the flywheel to be reduced to \(2\) rad s\(^{-1}\). [4]

Question 1:
1 | EITHER: Use C = Iα to find angular
acceleration α: α = – 48 × 0⋅3 / 18 [= – 0⋅8] M1 A1
(omitting minus sign loses this
A1 only)
Integrate or use ω 1 = ω 0 + αt to
find time t: t = (2 – 6)/α = 5 [s] M1 A1
OR: Use energy to find angle θ : θ = ½ 18(6 2 – 2 2 )/(48 × 0⋅3) [= 20] (M1 A1)
Use θ = ½(ω 0 +ω 1)t to find time
t: t = θ / ½(6 + 2) = 5 [s] (M1 A1) | 4 | [4]

A circular flywheel of radius $0.3$ m, with moment of inertia about its axis $18$ kg m$^2$, is rotating freely with angular speed $6$ rad s$^{-1}$. A tangential force of constant magnitude $48$ N is applied to the rim of the flywheel, in order to slow the flywheel down. Find the time taken for the angular speed of the flywheel to be reduced to $2$ rad s$^{-1}$.
[4]

\hfill \mbox{\textit{CAIE FP2 2012 Q1 [4]}}