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  • A disc rotates about its axis with its angular velocity varying with time s , find the n

A disc rotates about its axis with its angular velocity varying with time s \omega=2t+3, find the number of revolutions made by it from t=0s to t=2\pi s 

Option: 1

3


Option: 2

6


Option: 3

9


Option: 4

12


Answers (1)

best_answer

\omega=2 t+3

\frac{d \theta}{d t}=2 t+3

\int_0^\theta d \theta=\int_0^{2 \pi} 2 t d t+\int_0^{2\pi} 3 d t

\theta=(2 \pi)^2+3(2 \pi)

\theta=(2 \pi)[2 \pi+3]

\text { number of revolutions }=\frac{\theta}{2 \pi}=2 \pi+3

\begin{aligned} & =2 \times 3.14+3 \\ & =6.28+3 \\ & =9.28 \approx 9 \end{aligned}

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