IB Physics HL A.4.7 Point-mass moment of inertia Question Bank

Practise IB Physics HL A.4.7 by applying point-mass moment of inertia concepts to exam-style physics questions.

Exam points

identify the relevant physical quantity, model or diagram
apply the correct equation and units to the evidence
justify the result using conservation laws, forces or energy relationships

[Maximum number: 1]

A horizontal rigid bar of length 2 R is pivoted at its centre. The bar is free to rotate in a horizontal plane about a vertical axis through the pivot. A point particle of mass M is attached to one end of the bar and a container is attached to the other end of the bar.

A point particle of mass $\frac{M}{3}$ moving with speed v at right angles to the rod collides with the container and gets stuck in the container. The system then starts to rotate about the vertical axis.

The mass of the rod and the container can be neglected.

Figure for Question A.4.7 (HL)—Point-mass moment of inertia question 1 — IB Physics HL

Just after the collision the system begins to rotate about the vertical axis with angular velocity $\omega$ . Show that the angular momentum of the system is equal to $\frac{4}{3} M R^{2} \omega$ .

evidence of use of: $L=I \omega=\left(M R^{2}+\frac{M}{3} R^{2}\right) \omega$

a

iii

evidence of use of conservation of angular momentum, $\frac{M v R}{3}=\frac{4}{3} M R^{2} \omega$ «rearranging to get $\omega=\frac{V}{4 R}$ »

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A.4.7 (HL)—Point-mass moment of inertia question 1