Physics circular motion problem, totally stumped.?
Point on a rotating turntable 20.0 cm from the center accelerates from rest to 0.700 m/s in 1.75s. At t=1.25s, find magnitude of the radial acceleration, tangential acceleration and total acceleration.
Thanks in advance.
Point on a rotating turntable 20.0 cm from the center accelerates uniformly from rest to 0.700 m/s in 1.75s. At t=1.25s, find magnitude of the radial acceleration, tangential acceleration and total acceleration.
- Dr SpockLv 61 decade agoFavorite Answer
You forgot to state that it accelerated UNIFORMLY, that is at an unchanging rate. Without that stipulation, the answers would be indeterminate.
O.K. --- So, assuming UNIFORM ANGULAR ACCELERATION, the turntable accelerates to a rotational speed of 0.700 m/s in 1.75s. These figures are nicely adjusted to tell one that the acceleration rate of the (linear) rotational speed is
a = 0.700/1.75m/s^2 = 0.400m/s^2.
Thus the rotational speed at 1.25s will be v = at = 0.500m/s.
Then its INWARDLY DIRECTED radial acceleration, v^2 / r, will be (0.500)^2 / 0.20m/s^2 = 1.25m/s^2.
The tangential acceleration is still a = 0.400m/s^2.
Therefore the TOTAL ACCELERATION is [1.25^2 + 0.4^2]^(1/2)m/s^2 = 1.312...m/s^2. This total acceleration is directed inwards from the "forward tangential direction" at an angle arctan (1.25/0.4) = arctan (3.125) = 72.25... degrees.
Live long and prosper.