CAIE FP2 2012 June — Question 1 4 marks

Exam BoardCAIE
ModuleFP2 (Further Pure Mathematics 2)
Year2012
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicCircular Motion 1
TypeAngular kinematics – constant angular acceleration/deceleration
DifficultyModerate -0.3 This is a straightforward application of rotational dynamics using τ = Iα with constant torque. Students need to find torque (F × r), calculate angular deceleration, then use kinematics (ω = ω₀ + αt). It's slightly easier than average because it's a direct plug-and-chug problem with clearly given values and no conceptual complications, though the rotational context makes it non-trivial.
Spec6.05a Angular velocity: definitions6.05b Circular motion: v=r*omega and a=v^2/r

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:
AnswerMarks
1EITHER: 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
AnswerMarks Guidance
t: t = θ / ½(6 + 2) = 5 [s] (M1 A1)4 [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]}}