Question

A computer hard disk 8.0 cm in diameter is initially at rest. A small dot is painted on the edge of the disk. The disk accelerates at 680rad/s2 for 12s, then coasts at a steady angular velocity for another 12s.What is the speed of the dot at t = 1.0 s?

Answer 1

Explanation:

According to the kinematic equation,

   $\omega_{f} = \omega_{i} + at$

And, we are given

        $\omega_{i}$ = 0,      a = 680 $rad/s^{2}$

        t = 12 sec

Putting the given values into the above formula as follows.

       $\omega_{f} = \omega_{i} + at$

                    = $0 + 680 \times 12$

                    = 8160 rad/s

Also, we know that

           $\nu = r \times \omega$

                       = $\frac{0.08 m}{2} \times 8160 rad/s$

                       = 326.4 m/s

Thus, we can conclude that the speed of the dot at t = 1.0 sec is 326.4 m/s.