Question

A straight line is drawn on the surface of a 18-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?

Answer 1

v_r = 3.4 cm / s , v_t = 84.82 cm / s

Step-by-step explanation:

The speed of the insect has two components, one radial and the other tangential,

The radial component is the speed with which the insect moves with respect to the plate

v_r = 3.4 cm / s

The tangential component is given by

v = w r

Let's reduce the angular velocity to the SI system

w = 45 rpm (2π rad / 1 rev) (1 min / 60 s) = 4.712 rav / s

let's calculate

v = 4.712 18

v_t = 84.82 cm / s