Question

a rock is tied to the end of the string and swung in a circle with a radius of 1/2 meter. if the rock goes around once in 1/10 of a second what is the centripetal acceleration of the rock?

Answer 1

Answer:

1974.4328 m/s²

Explanation:

r = Radius = 0.5 m

t = Time taken = 0.1 second

Rotational speed

$v=\dfrac{2\pi r}{t}\\\Rightarrow v=\dfrac{2\pi 0.5}{0.1}\\\Rightarrow v=31.42\ m/s$

The centripetal acceleration is given by

$a_c=\dfrac{v^2}{r}\\\Rightarrow a_c=\dfrac{31.42^2}{0.5}\\\Rightarrow a_c=1974.4328\ m/s^2$

The centripetal acceleration of the rock is 1974.4328 m/s²