) The angular acceleration of the disk is defined by = 3t 2 + 12 rad/s, where t is in seconds. If the disk is originally rotating at 0 = 12 rad/s. a) Determine the angular motion when t = 2 s. b) Determine the magnitude of the velocity of point A on the disk when t = 2 s. c) Determine the normal and tangential components of acceleration of point A on the disk when t = 2 s.

a) , b) , c) ,

Explanation:

a) The angular motion is obtained by integrating the angular acceleration function twice:

The angular motion when t = 2 s. is:

b) Let be the distance between A and the rotation axis, measured in meters. The magnitude of the angular velocity when t = 2 s. is:

Finally, the magnitude of the velocity is:

c) The angular acceleration of the disk when t = 2 s. is:

Lastly, the normal and tangential components at point A are, respectively: