Question

always use significant figure rules. remember that these rules apply to all numbers that are measurements.
if an object moves in uniform circular motion in a circle of radius ( r = 1.00 ) meter, and the object takes ( 4.00 ) seconds to complete ten revolutions, calculate the centripetal acceleration.
( a=)_____ ( m / s^{2} )
( 247 mathrm{~m} / mathrm{s}^{2} )
( 98.7 mathrm{~m} / mathrm{s}^{2} )
( 3.14 mathrm{~m} / mathrm{s}^{2} )
( 78.5 mathrm{~m} / mathrm{s}^{2} )

Explanation:

Step1: Calcular la velocidad angular (\(\omega\))

La frecuencia \(f=\frac{n}{t}\), donde \(n = 10\) revoluciones y \(t=4.00\ s\). Entonces \(f=\frac{10}{4.00}=2.50\ Hz\).
La velocidad angular \(\omega = 2\pi f\), entonces \(\omega=2\pi\times2.50 = 5\pi\ rad/s\)

Step2: Calcular la aceleración centrípeta (\(a\))

La fórmula de la aceleración centrípeta es \(a=\omega^{2}R\). Dado que \(R = 1.00\ m\) y \(\omega=5\pi\ rad/s\), entonces \(a=(5\pi)^{2}\times1.00\)
\(a = 25\pi^{2}\times1.00\approx25\times9.87\times1.00=246.75\approx247\ m/s^{2}\)

Answer:

\(247\ m/s^{2}\)