Question

In a beyblade game, the beyblade has an initial angular speed of $180\text{rpm}$. It slows down and eventually comes to rest in a time of 5 minutes. The average angular acceleration of the beyblade is

• A. $\frac{\pi }{30}{\text{rad/s}}^2$
• B. $\frac{\pi }{40}{\text{rad/s}}^2$
• C. $\frac{\pi }{50}{\text{rad/s}}^2$
• D. $\frac{\pi }{70}{\text{rad/s}}^2$

Answer 1

The correct option is C $\frac{\pi }{50}{\text{rad/s}}^2$

Initial angular speed $=180\text{rpm}=180\times \frac{2\pi }{60}=6\pi \text{rad/s}$
Final angular speed $=0\text{rad/s}$
Time elapsed before the beyblade comes to rest $=5\text{min}=300\text{seconds}$
Average angular acceleration ${\alpha }_{avg}=\frac{\Delta \omega }{\Delta t}=\frac{{\omega }_f-{\omega }_i}{t_t-t_i}=\frac{0-6\pi }{300}=-\frac{\pi }{50}{\text{rad/s}}^2$
$\Rightarrow |{\alpha }_{avg}|=\frac{\pi }{50}{\text{rad/s}}^2$