A straight line is drawn on the surface of a 14-cm-radius turntable from the cen

Question

A straight line is drawn on the surface of a 14-cm-radius turntable from the center to the perimeter. A bug crawls along this line from the center outward as the turntable spins counterclockwise at a constant 45 rpm. Its walking speed relative to the turntable is a steady 3.4 cm/s.  Let its initial heading be in the positive x-direction, where the x- and y-directions are fixed relative to the laboratory.  As the bug reaches the edge of the turntable (still traveling at 3.4 cm/s radially, relative to the turntable) what are the x and y components of the velocity of the bug?

Explanation / Answer

r = 14 cm

w = 45 rpm

vr = 3.4cm/s

As the bug reaches the edge of the turntable (still traveling at 3.4 cm/s radially, relative to the turntable)

but tangential velocity will be= vt = wr = 45*14/60 = 10.5 cm/s

the time taken to travel 14cm radially = 14/3.4 = 1.117 sec

so angular displacement = w*t = 45 * 360 * 1.117/60 = 301.6 degrees, 360-301.6 = 58.41= A (say)

so the components in x and y direction will be

Vx = vr*cosA + vt*sinA = 10.725 cm/s

Vy = vt*cosA - vr*sinA = 2.604 cm/s

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