help with acceleration uniform circular motion?

Question

i did the lab to find acceleration by different mehtods
newton law a = T/m
and a= 4pi^2 r*f^2 , r= radius, f= frequency

why my answer is not the same

T= 43.14+/- .98%
m= 1.49 +/- .3%

r= .0565 +/- 1.8%
f= 11.5+/- .6%

Answer 1

Your question and assumptions are not at all clear. So I'm going to make the following assumptions.

First, you are looking for radial acceleration a along some radius of rotation r. This means something m is being swung around (by a string or rope?).

Second, uniform circular motion implies w = constant; where w is angular velocity = v/r; where v is tangential velocity and r is the radius of rotation.

Finally, from a = T/m, I'm assuming T is the tension in the presumed rope. In which case T = F = mv^2/r = mw^2 r, which is the centripetal force acting on m.

If all the assumptions are correct, then the radial acceleration mw^2 r/m = T/m = a = w^2 r; where w = 2pi f and f is the frequency in rotations per second and w is in radians per second.

As a is derived from T/m, there is no way a from T/m is not the same as a = (2pi f)^2 r unless you forgot to convert your angular velocity to radians. Remember, whenever dealing with both radius r and angles, the angles must be in radians for unit consistency.