IB Physics HL A 4 7 Hl Point Mass Moment of Inertia Questions

Calculate point-mass rotational inertia from perpendicular distances and apply it to compound-body angular momentum and rotational-motion problems.

Exam points

Identify the perpendicular distance from each point mass to the stated rotation axis.
Calculate and sum mr² contributions, including point masses combined with a supplied rod or body inertia.
Use the resulting point-mass system inertia in angular-momentum or rotational-motion calculations.

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Study A.4.7 (HL)—Point-mass moment of inertia conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

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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.

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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 $L=I\omega=\left(MR^{2}+\frac{M}{3}R^{2}\right)\omega=\frac{4}{3}MR^{2}\omega$

evidence of use of conservation of angular momentum, $\frac{MvR}{3}=\frac{4}{3}MR^{2}\omega$ , rearranging to get $\omega=\frac{v}{4R}$

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IB Physics HL A 4 7 Hl Point Mass Moment of Inertia Questions question 1