Question

The angular speed of the wheel of a vehicle is increased from $360$ rpm to $1200$ rpm in $14$ second Its angular acceleration is

• A. $2\pi \,rad/s^{2}$
• B. $28 \pi \,rad/s^{2}$
• C. $120\pi \,rad/s^{2}$
• D. $1 \,rad/s^{2}$

Answer 1

Answer: (A)

$\begin{array}{l} \omega_0=360 rpm =360 \times \frac{2 \pi}{60}=12 \pi rad / s \\ \omega=1200 rpm =1200 \times \frac{2 \pi}{60}=40 \pi rad / s \\ \text { By } \omega=\omega_0+\alpha t \\ 40 \pi=12 \pi+14(\alpha) \\ \alpha=\frac{28 \pi}{14} \alpha=2 \pi rad / s ^2 \end{array}$