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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 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

OR

equivalent of mass in rotational equations

 

OWTTE

[1 mark]

a.i.

ΔKE + Δrotational KE = ΔGPE

OR

\(\frac{1}{2}\)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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