A 16-cm-long straight line connects the center of a turntable to its edge. The turntable rotates counter-clockwise at 45 rpm. A bug crawls along the line from the turntable’s center at 3.5 cm s relative to the turntable. Assume it is initially moving in the positive x direction. At the moment the bug gets to the edge, what are the x and y components of the velocity of the bug?

Explanation:

Given that:

The radius of the table r = 16 cm  = 0.16 m

The angular velocity = 45 rpm

=

= 4.71 rad/s

However, the relative velocity of the bug with turntable is:

v = 3.5 cm/s = 0.035 m/s

Thus, the time taken to reach the bug to the end is:

t = 4.571s

So the angle made by the radius r  with the horizontal during the time the bug gets to the end is:

Now, the velocity components of the bug with respect to the table is:

Also, for the vertical component of the velocity