A point on a rotating turntable 20.0cm from the center accelerates from rest to final speed of 0.700m/s in 1.75s. At t=1.25s, find the magnitude and direction of
(a) the radial acceleration,
(b) the tangential acceleration,
(c) the total acceleration of the point.
a_r = v2/r
a_total = sqrt (a_t2 + a_rr)
The Attempt at a Solution
I'm having trouble understanding non-uniform circular motion.
At t=1.25s, this is before the particle reaches it's final velocity at 1.75s. If I found average acceleration over that time period (a = 0.7m/s / 1.75s =0.4m/s/s), can I then use this to find the velocity at 1.25s, then find the radial acceleration from there?
a_avg = 0.4m/s/s
v = a*t = (0.4m/s/s)(1.25s) = 0.5m/s
a_radial = v2 / r = (0.52) / 0.2m = 2.5m/s/s at point 1.25s
I'm not sure if it's right to use this average acceleration applied to any point between when the particle goes from it's initial (v=0m/s) to final velocity (0.7m/s). Since the particle is accelerating, I know that of course, the velocity changes, but does the magnitude of acceleration (0.4m/s/s) change moving around the circle?