There is an analogy between quantities in rotational and translational dynamics - AQA - A-Level Physics - Question 1 - 2017 - Paper 6

To find the total moment of inertia, we add the moment of inertia of the jib and the contributions from the trolley and load.

Using the formula: $I_{total} = I_{jib} + m imes r^2$ where:

• $I_{jib} = 2.6 \times 10^7 kg m^2$
• $m = 2.2 \times 10^3 kg$ (mass of trolley and load)
• $r = 35 m$ (distance from the axis of rotation)

Calculating the contribution: $I_{trolley/load} = 2.2 \times 10^3 kg \times (35 m)^2 = 2.2 \times 10^3 \times 1225 = 2.695 \times 10^6 kg m^2$

Finally, summing: $I_{total} = 2.6 \times 10^7 + 2.695 \times 10^6 = 2.8695 \times 10^7 kg m^2$

This confirms that the total moment of inertia is approximately $3 \times 10^7 kg m^2$.