A stone tied to the end of a string $80 ext{ cm}$ long is whirled in a horizontal circle with a con

Question

A stone tied to the end of a string $80	ext{ cm}$ long is whirled in a horizontal circle with a constant speed. If the stone makes $14$ revolutions in $25	ext{ s}$, what is the magnitude of the acceleration of the stone?

Professor PC Thomas Classes · Answer

Radius $R = 0.8	ext{ m}$. Frequency $
u = \frac{14}{25}	ext{ Hz}$. Angular speed $\omega = 2\pi
u = \frac{28\pi}{25}	ext{ rad/s}$. Centripetal acceleration $a_c = \omega^2 R = \left(\frac{28\pi}{25}ight)^2(0.8) \approx 9.87	ext{ m/s}^2 \approx 9.9	ext{ m/s}^2$.