Una rueda de 3.1 m de radio tiene una aceleración centrípeta de 72.7 m/s^2. Si el movimiento es circular uniforme, la frecuecia en r.p.m a la que rota es: Nota: respuesta precisa hasta la décima.
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Tenemos como datos:
![r=3.1\text{ m}\\
a_c=72.7\text{ m}/\text{s}^2\\ \\ \\
\text{Hallemos la velocidad angular: }\\ \\
\omega = \sqrt{\dfrac{a_c}{r}}=\dfrac{72.7}{3.1}=\dfrac{23.45~\text{rad}}{s}\\ \\ \\
\omega =\dfrac{23.45~\text{rad}\times 60}{60~s}\\ \\ \\
\omega =\dfrac{1407.097~\text{rad}}{\text{min}}\\ \\ \\
\omega =\dfrac{1407.097~\text{rad}}{\text{min}}\times\dfrac{2\pi}{2\pi}\\ \\ \\
\omega =\dfrac{(1407.097)/(2\pi)\times2\pi~\text{rad}}{\text{min}} r=3.1\text{ m}\\
a_c=72.7\text{ m}/\text{s}^2\\ \\ \\
\text{Hallemos la velocidad angular: }\\ \\
\omega = \sqrt{\dfrac{a_c}{r}}=\dfrac{72.7}{3.1}=\dfrac{23.45~\text{rad}}{s}\\ \\ \\
\omega =\dfrac{23.45~\text{rad}\times 60}{60~s}\\ \\ \\
\omega =\dfrac{1407.097~\text{rad}}{\text{min}}\\ \\ \\
\omega =\dfrac{1407.097~\text{rad}}{\text{min}}\times\dfrac{2\pi}{2\pi}\\ \\ \\
\omega =\dfrac{(1407.097)/(2\pi)\times2\pi~\text{rad}}{\text{min}}](https://tex.z-dn.net/?f=r%3D3.1%5Ctext%7B+m%7D%5C%5C%0Aa_c%3D72.7%5Ctext%7B+m%7D%2F%5Ctext%7Bs%7D%5E2%5C%5C+%5C%5C+%5C%5C%0A%5Ctext%7BHallemos+la+velocidad+angular%3A+%7D%5C%5C+%5C%5C%0A%5Comega+%3D+%5Csqrt%7B%5Cdfrac%7Ba_c%7D%7Br%7D%7D%3D%5Cdfrac%7B72.7%7D%7B3.1%7D%3D%5Cdfrac%7B23.45%7E%5Ctext%7Brad%7D%7D%7Bs%7D%5C%5C+%5C%5C+%5C%5C%0A%5Comega+%3D%5Cdfrac%7B23.45%7E%5Ctext%7Brad%7D%5Ctimes+60%7D%7B60%7Es%7D%5C%5C+%5C%5C+%5C%5C%0A%5Comega+%3D%5Cdfrac%7B1407.097%7E%5Ctext%7Brad%7D%7D%7B%5Ctext%7Bmin%7D%7D%5C%5C+%5C%5C+%5C%5C%0A%5Comega+%3D%5Cdfrac%7B1407.097%7E%5Ctext%7Brad%7D%7D%7B%5Ctext%7Bmin%7D%7D%5Ctimes%5Cdfrac%7B2%5Cpi%7D%7B2%5Cpi%7D%5C%5C+%5C%5C+%5C%5C%0A%5Comega+%3D%5Cdfrac%7B%281407.097%29%2F%282%5Cpi%29%5Ctimes2%5Cpi%7E%5Ctext%7Brad%7D%7D%7B%5Ctext%7Bmin%7D%7D)
![\omega =\dfrac{(1407.097)/(2\pi)\times\text{rev}}{\text{min}}\\ \\ \\
\omega =\dfrac{(1407.097)/(2\pi)\times\text{rev}}{\text{min}}\\ \\ \\
\omega =223.95~\dfrac{\text{rev}}{\text{min}}\\ \\ \\
\boxed{\boxed{\omega =223.9~\dfrac{\text{rev}}{\text{min}}}} \omega =\dfrac{(1407.097)/(2\pi)\times\text{rev}}{\text{min}}\\ \\ \\
\omega =\dfrac{(1407.097)/(2\pi)\times\text{rev}}{\text{min}}\\ \\ \\
\omega =223.95~\dfrac{\text{rev}}{\text{min}}\\ \\ \\
\boxed{\boxed{\omega =223.9~\dfrac{\text{rev}}{\text{min}}}}](https://tex.z-dn.net/?f=%5Comega+%3D%5Cdfrac%7B%281407.097%29%2F%282%5Cpi%29%5Ctimes%5Ctext%7Brev%7D%7D%7B%5Ctext%7Bmin%7D%7D%5C%5C+%5C%5C+%5C%5C%0A%5Comega+%3D%5Cdfrac%7B%281407.097%29%2F%282%5Cpi%29%5Ctimes%5Ctext%7Brev%7D%7D%7B%5Ctext%7Bmin%7D%7D%5C%5C+%5C%5C+%5C%5C%0A%5Comega+%3D223.95%7E%5Cdfrac%7B%5Ctext%7Brev%7D%7D%7B%5Ctext%7Bmin%7D%7D%5C%5C+%5C%5C+%5C%5C%0A%5Cboxed%7B%5Cboxed%7B%5Comega+%3D223.9%7E%5Cdfrac%7B%5Ctext%7Brev%7D%7D%7B%5Ctext%7Bmin%7D%7D%7D%7D)
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