A disk (radius = 8.0 cm) that rotates about a fixed axis starts from rest and accelerates at a constant rate to an angular velocity of 4.0 rad/s in 2.0 s. What is the magnitude of the total linear acceleration of a point on the rim of the disk at the instant when the angular velocity of the disk is 1.5 rad/s? A) 24 cm/s² B) 16 cm/s² C) 18 cm/s² D) 34 cm/s² E) 44 cm/s²

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Explanation:The total linear acceleration of a point on the rim of the disk is given by:$$a_t = a_c + a_t$$where:$$a_c = r\alpha$$is the centripetal acceleration,$$a_t = r\omega^2$$is the tangential acceleration,$$r$$is the radius of the disk,$$\alpha$$is the angular acceleration, and$$\omega$$is the angular velocity.At the instant when the angular velocity of the disk is 1.5 rad/s, the centripetal acceleration is:$$a_c = r\alpha = (0.08 \ m)(2.0 \ rad/s^2) = 0.16 \ m/s^2$$and the tangential acceleration is:$$a_t = r\omega^2 = (0.08 \ m)(1.5 \ rad/s)^2 = 0.18 \ m/s^2$$Therefore, the total linear acceleration is:$$a_t = a_c + a_t = 0.16 \ m/s^2 + 0.18 \ m/s^2 = 0.34 \ m/s^2$$

A Disk (Radius = 8