|MadSci Network: Physics|
FORCE = MASS * (SPEED^2)/RADIUS
I could solve for mass, if I can measure: RADIUS = length of rope, SPEED, and FORCE = whatever my scale is saying the force the rope is being pulled at is. I could simplify my SPEED measurement by using the relation that for a circular path:
SPEED = RADIUS * ANGULAR SPEED
ANGULAR SPEED is how fast the object completes an orbit in RADIANS. One orbit is 2*PI radians (about 6.28 per revolution). I could pick a spot to be my starting point of my circular orbit, like say a line on the ground and keep time of how long it takes me to turn all the way around and face that same direction while holding the rope which is attached to the unknown mass. This time = TIME of ONE ORBIT.
The final equation is:
FORCE = MASS * (RADIUS^2) * 6.28 /(TIME of ONE ORBIT).
Rearranging the equation:
MASS = FORCE * (TIME of ONE ORBIT) /( 6.28 * (RADIUS^2)).
And there are probably other ways someone can come up with to measure mass without gravity.
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