Physics

Problem

A bead moves uniformly on a circular track of radius

4\,\text{cm}

making

90

revolutions per minute. The foot of the perpendicular from the bead to a fixed diameter is observed. a. (i) Determine the linear speed

v_{c}

of the bead on the circle. b. (ii) Find the instantaneous speed

v_{s}

of its projection on the diameter when the bead is

45^{\circ}

away from that diameter. c. (iii) Obtain the ratio

v_{c}:v_{s}

for the instant described in part (ii) and comment on whether the projection can ever have the same speed as the bead.