Question

A point on a rotating turntable 19.0 cm from the center accelerates from rest to a final speed of 0.620 m/s in 1.70 s. At t = 1.22 s, find the magnitude and direction of each of the following. (a) the radial acceleration m/s2 toward the center away from the center in the direction of the rotation in a direction opposite to the rotation (b) the tangential acceleration m/s2 toward the center away from the center in the direction of the rotation in a direction opposite to the rotation (c) the total acceleration of the point m/s2 °

Answer 1

(b)

Tangential acceleration,

a_t = $\Delta$ v / $\Delta$ t

a_t = 0.62 / 1.70

a_t = 0.364 m/s^2

(a)

At t = 1.22 s

v = u + at

v = 0 + 0.364*1.22 = 0.4449 m/s

Radial acceleration,

a_r = v^2 / r

a_r = ( 0.4449)^2 / 0.19

a_r = 1.042 m/s^2

(c)

Total acceleration,

a = sqrt (0.364² + 1.042²)

a = 1.1039 m/s^2

Direction, $\theta$ = tan^-1 (1.042 / 0.364)

$\theta$ = 70.71 deg