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Date	May 2018	Marks available	1	Reference code	18M.3.SL.TZ2.6
Level	Standard level	Paper	Paper 3	Time zone	2
Command term	Outline	Question number	6	Adapted from	N/A

Question

A wheel of mass 0.25 kg consists of a cylinder mounted on a central shaft. The shaft has a radius of 1.2 cm and the cylinder has a radius of 4.0 cm. The shaft rests on two rails with the cylinder able to spin freely between the rails.

M18/4/PHYSI/SP3/ENG/TZ2/06

The stationary wheel is released from rest and rolls down a slope with the shaft rolling on the rails without slipping from point A to point B.

M18/4/PHYSI/SP3/ENG/TZ2/06.a

The wheel leaves the rails at point B and travels along the flat track to point C. For a short time the wheel slips and a frictional force F exists on the edge of the wheel as shown.

M18/4/PHYSI/SP3/ENG/TZ2/06.b

The moment of inertia of the wheel is 1.3 × 10^–4 kg m². Outline what is meant by the moment of inertia.

[1]

a.i.

In moving from point A to point B, the centre of mass of the wheel falls through a vertical distance of 0.36 m. Show that the translational speed of the wheel is about 1 m s^–1 after its displacement.

[3]

a.ii.

Determine the angular velocity of the wheel at B.

[1]

a.iii.

Describe the effect of F on the linear speed of the wheel.

[2]

b.i.

Describe the effect of F on the angular speed of the wheel.

[2]

b.ii.

Markscheme

an object’s resistance to change in rotational motion

equivalent of mass in rotational equations

OWTTE

[1 mark]

a.i.

ΔKE + Δrotational KE = ΔGPE

$\frac{1}{2}$ mv² + $\frac{1}{2}$ I $\frac{{{v^2}}}{{{r^2}}}$ = mgh

$\frac{1}{2}$ × 0.250 × v² + $\frac{1}{2}$ × 1.3 × 10^–4 × $\frac{{{v^2}}}{{1.44 \times {{10}^{ - 4}}}}$ = 0.250 × 9.81 × 0.36

v = 1.2 «m s^–1»

[3 marks]

a.ii.

ω «= $\frac{{1.2}}{{0.012}}$ » = 100 «rad s^–1»

[1 mark]

a.iii.

force in direction of motion

so linear speed increases

[2 marks]

b.i.

force gives rise to anticlockwise/opposing torque on

wheel ✓ so angular speed decreases ✓

OWTTE

[2 marks]

b.ii.

Examiners report

[N/A]

a.i.

[N/A]

a.ii.

[N/A]

a.iii.

[N/A]

b.i.

[N/A]

b.ii.

Syllabus sections

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

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