-- The string is 1 m long. That's the radius of the circle that the mass is traveling in. The circumference of the circle is (π) x (2R) = 2π meters .
-- The speed of the mass is (2π meters) / (0.25 sec) = 8π m/s .
-- Centripetal acceleration is V²/R = (8π m/s)² / (1 m) = 64π^2 m/s²
-- Force = (mass) x (acceleration) = (1kg) x (64π^2 m/s²) =
64π^2 kg-m/s² = 64π^2 N = about <span>631.7 N .
</span>That's it. It takes roughly a 142-pound pull on the string to keep 1 kilogram revolving at a 1-meter radius 4 times a second !<span> </span>If you eased up on the string, the kilogram could keep revolving in the same circle, but not as fast.
You also need to be very careful with this experiment, and use a string that can hold up to a couple hundred pounds of tension without snapping. If you've got that thing spinning at 4 times per second and the string breaks, you've suddenly got a wild kilogram flying away from the circle in a straight line, at 8π meters per second ... about 56 miles per hour ! This could definitely be hazardous to the health of anybody who's been watching you and wondering what you're doing.
