IB Physics HL A 4 6 Hl Moment of Inertia Questions

Use moment of inertia to relate mass distribution, torque, angular acceleration, rotational energy and rolling behaviour in extended bodies.

Exam points

Define moment of inertia as rotational resistance and use I=Σmr² with perpendicular distance from the axis.
Calculate the moment of inertia of rods, cylinders and compound bodies from the supplied model and dimensions.
Compare how mass distribution changes moment of inertia and therefore angular acceleration or rolling behaviour.

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Study A.4.6 (HL)—Moment of inertia conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

[Maximum number: 3]

A uniform cylinder, of mass M and length L, has a moment of inertia of $\frac{1}{12} M L^{2}$ when rotated about an axis through its centre.

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(a)

Outline what is meant by moment of inertia.

[ 1 ]

quotes $\mathrm{I}=\Sigma \mathrm{mr}^{2}$ with r= «perpendicular» distance to axis

OR

resistance to change in rotation

OR

ratio of torque «applied» to angular acceleration

OR

analog to mass in rotational mechanics

In MP1, accept r= radius.

In MP2, do not accept resistance to rotation.

In MP3 accept the expression as a formula if both symbols identified.

(b)

Two identical cylinders, each of mass M and length L, are connected end to end. Show that the moment of inertia when these cylinders are rotated about their combined centre is $\frac{2}{3} M L^{2}$ .

[ 1 ]

$\frac{1}{12} 2 M(2 L)^{2}=<\frac{8}{12} M L^{2}=\frac{2}{3} M L^{2}>\vee$

(c)

A two-blade propeller can be modelled using the two-cylinder arrangement in (a)(iii).

The following data for the two-blade propeller are available:
Length of each blade: 0.60 m
Mass of each blade: 2.2 kg
Show that the moment of inertia of the two-blade propeller is about $0.5 \mathrm{~kg} \mathrm{~m}^{2}$ .

[ 1 ]

$\frac{2}{3} \times 2.2 \times 0.6^{2}$

OR
$\frac{1}{12} \times 4.4 \times 1.2^{2}$

OR

0.53 «kg $\mathrm{m}^{2}$ »

Answer of $0.5 \mathrm{~kg} \mathrm{~m}^{2}$ given, so award the
mark if candidates show a correct full substitution OR the value with an extra significant figure

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IB Physics HL A 4 6 Hl Moment of Inertia Questions question 1

Question (a)

Question (b)

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