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 acceleration. What is the radial acceleration of a point 4.0 cm from the center at the time 15.0 seconds from the start? A) 0.5 m/s² B) 1.0 m/s² C) 1.8 m/s² D) 2.0 m/s² E) 2.6 m/s²

Question

Quizplus · Accepted Answer

The radial (centripetal) acceleration $a_r$ at a distance $r$ from the center of a rotating object with angular velocity $\omega$ is given by $a_r = r\omega^2$. At 15.0 seconds, the CD is rotating at 5.0 rad/sec, and we are asked for the radial acceleration at a point 4.0 cm (0.04 m) from the center. Thus, $a_r = 0.04 m \times (5.0 rad/sec)^2 = 0.04 m \times 25.0 rad^2/sec^2 = 1.0 m/s^2$.

A CD with a Diameter of 12