torque calculation

Question

A torque of 12 N·m acts on a wheel with I = 3 kg·m² from rest. Angular acceleration?

RankGuru · Accepted Answer

1. **Rotational Newton's Law**: $\vec{\tau} = I \vec{\alpha}$. This is the angular analogue of $F = ma$.
2. **Isolate $\alpha$**: $\alpha = \frac{\tau}{I}$.
3. **Substitute values**:
   - Torque $\tau = 12 \text{ N·m}$
   - Moment of Inertia $I = 3 \text{ kg·m}^2$
4. **Calculation**:
   - $\alpha = 12 / 3 = 4 \text{ rad/s}^2$.
5. **Conclusion**: The angular acceleration produced is **$4$ rad/s²**.

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torque calculation

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