a twirlers baton is 0.76 m long and spins around its center. the end of the baton has a centripetal…

Explanation:

Step1: Find the radius

The baton spins around its center, so the radius $r$ is half of its length. Given length $L = 0.76$ m, then $r=\frac{L}{2}=\frac{0.76}{2}= 0.38$ m.

Step2: Use centripetal - acceleration formula to find angular velocity

The centripetal - acceleration formula is $a_c = r\omega^{2}$. We know $a_c = 47.8$ m/s² and $r = 0.38$ m. Rearranging for $\omega$, we get $\omega=\sqrt{\frac{a_c}{r}}$. Substituting the values, $\omega=\sqrt{\frac{47.8}{0.38}}\approx\sqrt{125.79}\approx11.21$ rad/s.

Step3: Find the period

The relationship between angular velocity $\omega$ and period $T$ (time to complete one spin) is $\omega=\frac{2\pi}{T}$. Rearranging for $T$, we get $T = \frac{2\pi}{\omega}$. Substituting $\omega\approx11.21$ rad/s, $T=\frac{2\pi}{11.21}\approx\frac{6.28}{11.21}\approx0.56$ s.

Answer:

0.56 s