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  • A wheel at rest its angular velocity increases uniformly with time and becomes  Rad per second after <img alt="5" src="

A wheel at rest its angular velocity increases uniformly with time and becomes 80 Rad per second after 5 second. The total angular displacement is-

Option: 1

800 \ rad


Option: 2

400 \ rad


Option: 3

200\ rad


Option: 4

100 \ rad


Answers (1)

best_answer

Given, \\ \begin{aligned} & \omega_0=0, \alpha=\text { constant } \\ & \omega=80 \mathrm{rad} / \mathrm{s} \end{aligned} \\\\ Use\ Newton's\ equation - \\ \begin{aligned} v & =u+a t \\ \omega & =\omega_0+\alpha t \\ 80 & =0+\alpha \cdot 5 \\ \alpha & =\frac{80}{5}=16\ \mathrm{Rad} / \mathrm{s}^2 \end{aligned}
Angular dispiacement ,
 \begin{aligned} & \theta=\omega_0 t+\frac{1}{2} \alpha\ t^2 \\ & \theta=0 \times 5+\frac{1}{2} \times 16 \times 25 \\ & \theta=8 \times 25 \end{aligned}
\Theta = 200 \ rad

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Nehul

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