Answer
(a) The initial speed is $1.0 \times 10^5~m/s$
(b) The magnitude of the tangential acceleration is $0.080~m/s^2$
(c) The maximum radial acceleration is $5.0\times 10^{10}~m/s^2$
Work Step by Step
(a) For a point at the end of the rotor, we can find the initial speed:
$v_0 = \omega_0~r$
$v_0 = (5.0\times 10^5~rad/s)(0.200~m)$
$v_0 = 1.0\times 10^5~m/s$
The initial speed is $1.0 \times 10^5~m/s$
(b) For a point at the end of the rotor, we can find the magnitude of the tangential acceleration:
$a_t = \alpha~r$
$a_t = (0.40~rad/s^2)(0.200~m)$
$a_t = 0.080~m/s^2$
The magnitude of the tangential acceleration is $0.080~m/s^2$
(c) The maximum radial acceleration occurs when the angular speed is at a maximum:
$a_c = \omega^2~r$
$a_c = (5.0\times 10^5~rad/s)^2(0.200~m)$
$a_c = 5.0\times 10^{10}~m/s^2$
The maximum radial acceleration is $5.0\times 10^{10}~m/s^2$
