DP Physics (last assessment 2024)

Question 18M.3.SL.TZ2.6

Date	May 2018	Marks available	[Maximum mark: 9]	Reference code	18M.3.SL.TZ2.6
Level	SL	Paper	3	Time zone	TZ2
Command term	Describe, Determine, Outline, Show that	Question number	6	Adapted from	N/A

[Maximum mark: 9]

18M.3.SL.TZ2.6

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

(a.i)

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

[1]

Markscheme

an object’s resistance to change in rotational motion

equivalent of mass in rotational equations

OWTTE

[1 mark]

(a.ii)

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]

Markscheme

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.iii)

Determine the angular velocity of the wheel at B.

[1]

Markscheme

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

[1 mark]

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