# Chapter 4 - Kinematics in Two Dimensions - Exercises and Problems: 34

(a) $a_c = 40~m/s^2$ (b) $a_c = 80~m/s^2$

#### Work Step by Step

(a) $a_c = \omega^2~r$ If $r$ is doubled, then the centripetal acceleration is also doubled. The centripetal acceleration of the speck of dust that is twice as far away from the center is $40~m/s^2$ (b) $(2\omega)^2~r = 4\omega^2~r = 4~a_c$ The centripetal acceleration would be $80~m/s^2$

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