Moment of inertia

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Rotation's version of **mass** — resistance to angular acceleration: $I = \sum m r^{2}$. Unit: **kg m²**.

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Because r is **squared** in I = Σmr² — doubling the distance quadruples that part's contribution.

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$\tau = I\alpha$ (torque = moment of inertia × angular acceleration).

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The **hoop** (I = MR²); the disc is ½MR².

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$I = \tfrac{1}{2}MR^{2}$ (given in the question).

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$I = MR^{2}$ — all the mass is at radius R.

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No — the **exam gives them**; recognise and substitute.

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$\alpha = \tau / I$ — rearranged from τ = Iα.

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**Torque** τ.

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Yes — the same object has different I about different axes.

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**kg m²**.