angular displacement

Question

With the same data (α = 4 rad/s²), angular displacement in first 5 s?

RankGuru · Accepted Answer

1. **Kinematic Equation**: The angular displacement ($	heta$) is given by $	heta = \omega_0 t + \frac{1}{2} \alpha t^2$.
2. **Data**:
   - $\omega_0 = 0$
   - $\alpha = 4 	ext{ rad/s}^2$
   - $t = 5 	ext{ s}$
3. **Substitution**:
   - $	heta = 0 + \frac{1}{2} 	imes 4 	imes (5)^2$
   - $	heta = 2 	imes 25$
   - $	heta = 50 	ext{ rad}$.
4. **Check**: Alternatively, use $	heta = \left(\frac{\omega_0 + \omega}{2}ight)t = \left(\frac{0 + 20}{2}ight) 	imes 5 = 10 	imes 5 = 50 	ext{ rad}$.

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