IB Physics HL A.4.6 Moment of inertia

[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

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

Question (a)

Question (b)

Question (c)