A CD with a diameter of 12.0 cm starts from rest and with a constant angular acc

Question

A CD with a diameter of 12.0 cm starts from rest and with a constant angular acceleration of 1.0 rad/sec2 acquires an angular velocity of 5.0 rad/sec. The CD continues rotating at 5.0 rad/sec for 15.0 seconds and then slows to a stop in 12.0 second with a constant angular deceleration. What is the total acceleration of a point 4.0 cm from the center at the time 2.0 seconds from the start?

A. .450 m/s^2

B. .314 m/s^2

C. .215 m/s^2

D. .165 m/s^2

E. .100 m/s^2

Does anyone know the answer and can you provide work to prove this answer?

Explanation / Answer

at = alpha.r = 1 x 0.04 = 0.04 m/s2

ac = w^2.r = (1 x 2)^2 . 0.04 = 0.16 m/s2

atotal = sqrt(at^2 + ac^2 ) = 0.165 m/s2   Ans . D

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