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Date	November 2016	Marks available	4	Reference code	16N.3.SL.TZ0.8
Level	Standard level	Paper	Paper 3	Time zone	0 - no time zone
Command term	Calculate and Determine	Question number	8	Adapted from	N/A

Question

A flywheel consists of a solid cylinder, with a small radial axle protruding from its centre.

The following data are available for the flywheel.

Flywheel mass M	= 1.22 kg
Small axle radius r	= 60.0 mm
Flywheel radius R	= 240 mm
Moment of inertia	= 0.5 MR²

An object of mass m is connected to the axle by a light string and allowed to fall vertically from rest, exerting a torque on the flywheel.

The velocity of the falling object is 1.89 m s^–1 at 3.98 s. Calculate the average angular acceleration of the flywheel.

[2]

Show that the torque acting on the flywheel is about 0.3 Nm.

[2]

(i) Calculate the tension in the string.

(ii) Determine the mass m of the falling object.

[4]

Markscheme

ALTERNATIVE 1

${\omega _{{\text{final}}}} = \frac{v}{r} = 31.5$ «rad s^–1»

« $\omega = {\omega _o} + \alpha t$ so» $\alpha = \frac{\omega }{t} = \frac{{31.5}}{{3.98}} = 7.91$ «rad s^–2»

ALTERNATIVE 2
$a = \frac{{1.89}}{{3.98}} = 0.4749$ «m s^–2»

$\alpha = \frac{a}{r} = \frac{{0.4749}}{{0.060}} = 7.91$ «rad s^–2»

Award [1 max] for r = 0.24 mm used giving $\alpha$ = 1.98 «rad s^–2».

$\Gamma = \frac{1}{2}{\rm{M}}{{\rm{R}}^{\rm{2}}}\alpha = \frac{1}{2} \times 1.22 \times {0.240^2} \times 7.91$

= 0.278 «Nm»

At least two significant figures required for MP2, as question is a “Show”.

${F_T} = \frac{\Gamma }{r}$

${F_T} = 4.63$ «N»

Allow 5 «N» if Γ= 0.3 Νm is used.

${F_T} = mg - ma$ so $m = \frac{{4.63}}{{9.81 - 0.475}}$
m = 0.496 «kg»

Allow ECF

Examiners report

[N/A]

Syllabus sections

Option B: Engineering physics » Option B: Engineering physics (Core topics) » B.1 – Rigid bodies and rotational dynamics

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