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When a bus moves suddenly, the person standing in it tilts backwards. This concept is explained using inertia(tendency of body to resist change in its state of motion) but when the bus moves suddenly, can't we also say that the torque applied due to frictious force on our feet causes our upper body to move backwards?

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In the inertial (non-accelerating) frame of reference, you can analyse the pendulum as if it were any other object in an inertial frame of reference. You can look at the net forces acting on the pendulum and determine the angle that these forces would be in equilibrium.

In this case, instead of considering the pendulum as accelerating with the container, and using inertial forces to find the angle, you would need to analyze how the container imparts force onto the pendulum when it accelerates. This force is what causes the pendulum to begin it's movement with the vehicle.

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The free body diagram is on the right with the tension in the string $\vec T$ and the weight of the bob $m\,\vec g$.

$\vec F = \vec T + m\,\vec g$ and $\vec F = m\,\vec a$

enter image description here

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