# Chapter 5 - Problems - Page 188: 54

(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 $5.0\times 10^{10}~m/s^2$

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